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Costin_Costin_Jauslin_Lebowitz_2019.tex
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\documentclass{ian}
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\usepackage{graphicx}
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\usepackage{array}
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\begin{document}
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\hbox{}
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\hfil{\bf\LARGE
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Exact solution of the Schr\"odinger equation\par
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\hfil for photoemission from a metal\par
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}
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\vfill
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\hfil{\bf\large Ovidiu Costin}\par
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\hfil{\it Department of Mathematics, The Ohio State University}\par
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\hfil{\tt\color{blue}\href{mailto:costin.9@osu.edu}{costin.9@osu.edu}}\par
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\vskip20pt
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\hfil{\bf\large Rodica Costin}\par
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\hfil{\it Department of Mathematics, The Ohio State University}\par
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\hfil{\tt\color{blue}\href{mailto:costin.10@osu.edu}{costin.10@osu.edu}}\par
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\vskip20pt
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\hfil{\bf\large Ian Jauslin}\par
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\hfil{\it Department of Physics, Princeton University}\par
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\hfil{\tt\color{blue}\href{mailto:ijauslin@princeton.edu}{ijauslin@princeton.edu}}\par
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\vskip20pt
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\hfil{\bf\large Joel L. Lebowitz}\par
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\hfil{\it Department of Mathematics and Physics, Rutgers University}\par
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\hfil{\tt\color{blue}\href{mailto:lebowitz@math.rutgers.edu}{lebowitz@math.rutgers.edu}}\par
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\vskip20pt
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\vfill
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\hfil {\bf Abstract}\par
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\medskip
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{\small
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We solve rigorously the time dependent Schr\"odinger equation describing electron emission from a metal surface by a laser field perpendicular to the surface.
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We consider the system to be one-dimensional, with the half-line $x<0$ corresponding to the bulk of the metal and $x>0$ to the vacuum.
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The laser field is modeled as a classical electric field oscillating with frequency $\omega$, acting only at $x>0$.
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We consider an initial condition which is a stationary state of the system without a field, and, at time $t=0$, the field is switched on.
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We prove the existence of a solution $\psi(x,t)$ of the Schr\"odinger equation for $t>0$, and compute the surface current.
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The current exhibits a complex oscillatory behavior, which is not captured by the ``simple'' three step scenario.
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As $t\to\infty$, $\psi(x,t)$ converges with a rate $t^{-\frac32}$ to a time periodic function with period $\frac{2\pi}{\omega}$ which coincides with that found by Faisal, Kami\'nski and Saczuk (Phys Rev A {\bf 72}, 023412, 2015).
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However, for realistic values of the parameters, we have found that it can take quite a long time (over 50 laser periods) for the system to converge to its asymptote.
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Of particular physical importance is the current averaged over a laser period $\frac{2\pi}\omega$, which exhibits a dramatic increase when $\hbar\omega$ becomes larger than the work function of the metal, which is consistent with the original photoelectric effect.
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}
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\vfill
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\tableofcontents
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\vfill
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\eject
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\setcounter{page}1
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\pagestyle{plain}
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\section{Introduction}
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\indent In this note, we continue our investigation of the exact solution of the time-dependent Schr\"odinger equation describing the emission of electrons from a metal surface by an electric field \cite{CCe18}.
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We use the Sommerfeld model of quasi-free electrons with a Fermi distribution of energies, confined by a step potential $U=\mathcal E_F+W$, where $\mathcal E_F$ is the Fermi energy and $W$ is the work function of the metal.
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This setup is commonly used as a simple model for the process of emission, both for a constant field and an oscillating field \cite{FN28,YGR11,Fo16,Je17}.
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In both cases one focuses attention on electrons, part of the Fermi sea, with energy $\frac12k^2$ (in atomic units), moving from the left towards the metal surface at $x=0$.
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These are described by a wave function $e^{ikx}$, $k>0$, $x<0$.
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When the electrons reach the metal surface they are either reflected or transmitted through the barrier.
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\bigskip
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\indent The time evolution of the wave function of an electron in such a beam is described by the one dimensional Schr\"odinger equation,
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\begin{equation}
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i\partial_t\psi(x,t)=H(x,t)\psi(x,t)=-\frac12\Delta\psi(x,t)+\Theta(x)(U-Ex\cos(\omega t))\psi(x,t)
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\label{schrodinger}
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\end{equation}
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where $\Theta(x)=0$ for $x<0$ and $\Theta(x)=1$ for $x>0$, $E$ is the electric field perpendicular to the surface, $\frac\omega{2\pi}$ is the frequency and we are using atomic units $\hbar=m=1$.
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Here, we ignore the carrier wave and Shottky effect.
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We also only focus on the direction that is orthogonal to the metal surface, ignoring the other two directions \cite{KSH11}.
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\indent In the absence of an external field, $E=0$, the Schr\"odinger equation (\ref{schrodinger}) has a ``stationary" solution $e^{-i\frac12k^2t}\varphi_0(x)$ in which there is, for $k^2<2U$, a reflected beam of the same energy and intensity as the incoming beam $e^{ikx}$ and an evanescent, exponentially decaying tail on the right,
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\begin{equation} \label{initial}
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\varphi_0(x)=
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\left\{\begin{array}{ll}
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e^{ikx}+R_0e^{-ikx}&\mathrm{for\ }x<0\\
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T_0e^{- \alpha x}&\mathrm{for\ }x>0
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\end{array}\right.
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\end{equation}
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Using the continuity of $\psi$ and its derivative at $x=0$ yields
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\begin{equation}
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\alpha:=\sqrt{2U-k^2}
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,\quad
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1+R_0=T_0=\frac{2ik}{ik-\sqrt{2U-k^2}}
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.
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\end{equation}
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The current,
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\begin{equation}
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j(x,t):=\mathcal Im(\psi^*(x,t)\partial_x\psi(x,t))
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\end{equation}
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is zero and no electrons leave the metal.
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Note that $\varphi_0$ is not square integrable, which will complicate matters when it comes to solving the Schr\"odinger equation.
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\indent If we turn on a constant field, $E>0, \ \omega=0$, at $t=0$, the Schr\"odinger equation has a ``stationary'' solution ${\rm e}^{-\frac 12 k^2 t}\varphi_{E}(x)$ with $\varphi_E$ satisfying the equation
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\begin{equation}
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\frac12k^2\varphi_E=-\frac12\frac{\partial^2}{\partial x^2}\varphi_E+\Theta(x)(U-Ex)\varphi_E
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\end{equation}
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with incident beam $\Theta(-x)e^{ikx}$.
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This equation was solved by Fowler and Nordheim \cite{FN28} in 1928 to describe the quantum tunneling of electrons through a triangular barrier.
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Their solution, with some corrections, is commonly used to describe the stationary current produced by a field $E$ acting on the surface of a metal \cite{Je17}.
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\bigskip
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\indent In \cite{CCe18} we solved the time-dependent Schr\"odinger equation (\ref{schrodinger}) with initial condition $\varphi_0(x)$ for the constant field.
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We showed that $\psi(x,t)$ converges, as $t\to\infty$, to the Fowler-Nordheim (FN) solution ${\rm e}^{-\frac 12 k^2 t}\varphi_{E}(x)$
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The exact rate of convergence is $t^{-\frac32}$.
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The ``effective'' time of approach to the FN solution was found to be, for realistic values of the parameters, of the order of femtoseconds.
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\indent Here, we investigate solutions of (\ref{schrodinger}) with $E>0$, $\omega>0$, $\psi(x,0)=\varphi_0(x)$ as given in (\ref{initial}).
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Since we are interested in describing situations in which the laser is turned on for only a short time, with pulses as short as a few periods, understanding the role of the initial state is important.
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This problem turns out to be considerably more difficult than the constant field case, $\omega=0$.
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\bigskip
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\indent There are several studies in the literature about the solution of the time-dependent Schr\"odinger equation, see \cite{KLe18} and references therein.
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The method most often used is the Crank-Nicolson \cite{CN47} numerical scheme.
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In the case treated here, however, as we will discuss in more detail in the following, because of the discontinuity in the potential at $x=0$, the Crank-Nicolson algorithm is actually inaccurate for short times.
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We will introduce an alternative scheme that does not suffer from the discontinuity of the potential.
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\indent Of particular note is the work by Yalunin, Gulden and Roper \cite{YGR11}, where the initial condition and potential are the same as in (\ref{schrodinger}) and (\ref{initial}).
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Our result is quite different from theirs for short time, but the values we obtain at longer times seem to agree qualitatively with those obtained in \cite{YGR11} for short times.
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Furthermore, in \cite{YGR11}, there does not seem to be a distinction between long and short times, whereas we find that for some important physical quantities, like the current averaged over a laser period, one has to wait many periods to be close to the asymptotic value.
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\bigskip
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\indent We look for an exact solution of (\ref{schrodinger}) for $t>0$ such that $\psi(x,t)$ and its derivative $\partial_x\psi(x,t)$ are continuous at $x=0$ and be bounded for $|x|\to\infty$.
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To do this, we first obtain the solutions for $x<0$ and for $x>0$ with general initial conditions and unknown time dependent boundary conditions $\psi(0,t)=\psi_0(t)$ and $\partial_x\psi(x,t)|_{x=0}=\psi_{x,0}(t)$.
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A solution of (\ref{schrodinger}) with appropriate $x\to\pm\infty$ conditions will exist if and only if we can match these boundary conditions coming from the right and from the left.
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This approach to solving such an equation as (\ref{schrodinger}) goes under the general name of initial-boundary-value (IBV) problem, developed in particular by Fokas for these types of problems \cite{Fo97,Ry18}.
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\indent We prove the existence of a solution of (\ref{schrodinger}) by showing that a necessary and sufficient condition for this is that $\psi_0(t)$ satisfies an integral equation.
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The existence of the solution $\psi(x,t)$ for all $x$ and $t$ then follows from the proof that this integral equation has a unique solution, which we provide.
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Expressions for $\psi$ and for the current $j(x,t)$ are given by explicit integrals involving $\psi_0(t)$ \cite{CCe}.
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These can be evaluated numerically.
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To do so accurately for both short and moderate times, we developed a numerical scheme which goes beyond the Crank-Nicolson algorithm \cite{CN47}, see section\,\ref{Sec3}.
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\bigskip
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\indent $\psi(x,t)$ has the long time form $e^{-i\frac12k^2t}\mathcal U(x,t)$, where $\mathcal U$ is (up to a phase) the periodic in time solution of (\ref{schrodinger}) derived by Faisal et al \cite{FKS05,ZL16}.
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We note that Faisal et al. did not prove the existence of a solution to their infinite set of equations.
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Instead, they solved numerically a truncated set of these equations.
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Our results prove the existence of such a solution.
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\indent The approach to this asymptotic form $\mathcal U$ goes like $t^{-\frac32}$.
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$\mathcal{U}(x,t)$ consists of resonance terms which can be associated, as was done in \cite{FKS05}, with the absorption (emission) of different number of photons, see Section\,\ref{longtime}.
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These resonances show up dramatically when considering the dependence of the average current on $\omega$ in the vicinity of $\omega_c=W$, as seen in early experiments on the photoelectric effect where light with frequency $\omega>\omega_c$ was necessary to get electron emission.
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\section{Existence of solutions of the Schr\"odinger equation}
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\indent Here we give an outline of the proof derived in \cite{CCe}. To simplify the notations we rescale: let
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\begin{equation}\label{rescale}
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\bar t=\omega t,\ \ \bar x=\sqrt{2\omega}x,\ \ \bar U=U\omega^{-1},\ \ \bar E=E\omega^{-3/2}2^{-1/2}
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\end{equation}
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Equation (\ref{schrodinger}) becomes
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\begin{equation}\label{eq12}
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i\partial_{\bar t}\psi(\bar x,\bar t)=-\partial^2_{\bar x}\psi(\bar x,\bar t)+\Theta(\bar x)\left( \bar U-2\bar E \bar x\cos(\bar t)\right)\psi(\bar x,\bar t)
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\end{equation}
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As mentioned earlier, we will solve (\ref{eq12}) with the general initial condition
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$\psi(\bar x,0):=f(\bar x)$ separately for $\bar x<0$, $\psi_-(\bar x,\bar t)$ and for $\bar x>0$, $\psi_+(\bar x,\bar t)$, and then match the values of $\psi_\pm(0,\bar t)$ and $\partial_{\bar x}\psi_\pm(0,\bar t)$.
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\bigskip
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\indent To obtain these solutions we first go from $\bar x$ to Fourier space.
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We write
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\begin{equation}
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\hat\psi(\xi,\bar t)=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty d\bar x\ e^{-i\bar x\xi}\psi(\bar x,\bar t)
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=\hat\psi_-(\xi,\bar t)+\hat\psi_+(\xi,\bar t)
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\end{equation}
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where $\hat\psi_\pm$ is the half-line Fourier transform along $\pm \bar x>0$.
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\bigskip
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\indent The equation for $\hat\psi_-(\xi,\bar t)$ has the form
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\begin{equation}\label{eq5}
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i\frac{\partial \hat{\psi}_-}{\partial\bar t}=\xi^2 \hat{\psi}_-- \frac1{\sqrt{2\pi}} \psi_{\bar x,0}(\bar t)-i\xi \frac1{\sqrt{2\pi}} \psi_0(\bar t)
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\end{equation}
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where
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\begin{equation}
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\psi_0(\bar t):=\psi(0,\bar t)
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,\quad
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\psi_{\bar x,0}(\bar t):=\partial_{\bar x}\psi(0,\bar t)
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\end{equation}
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are treated as unknown functions to be determined later by the matching conditions.
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The solution of (\ref{eq5}) is given by
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\begin{equation} \label{psim}
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\hat{\psi}_-(\xi,\bar t)= {\rm e}^{-i\xi^2\bar t}\left\{ C_-(\xi) + \frac1{\sqrt{2\pi}} \int_0^{\bar t} {\rm e}^{i\xi^2\bar s}\ \left[ i\psi_{\bar x,0}(\bar s)-\xi \psi_0(\bar s) \right]\, d\bar s\right\}
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\end{equation}
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where
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$C_-(\xi)=\int_{-\infty}^0{\rm e}^{-i\bar x\xi}f(\bar x)\, d\bar x$.
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Inverting the Fourier transform we obtain, for all $\bar x<0$,
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\begin{equation}\label{psiminus}
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{\psi}_-(\bar x,\bar t)=h_-(\bar x,\bar t)+ \frac i{{2\pi}} \int_0^{\bar t} d\bar s\, \psi_{\bar x,0}(\bar s) H_0(\bar t-\bar s,\bar x)+ \frac i{{2\pi}} \int_0^{\bar t} d\bar s\, \psi_0(\bar s) \, \partial_{\bar x}H_0(\bar t-\bar s,\bar x)
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\end{equation}
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where
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$$
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h_-(\bar x,\bar t) =\frac 1{{2\pi}}\int_{-\infty}^0 f(\bar y) H_0(\bar t,\bar x-\bar y)\, d\bar y,
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\quad
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H_0(\bar t,\bar r)= \frac {\sqrt{\pi}}{\sqrt{i}{\sqrt{\bar t}}} {\rm e}^{\frac{i\bar r^2}{4\bar t}}
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$$
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\bigskip
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\indent The equation for $\hat{\psi}_+(\xi,\bar t)$ is given by
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$$i\frac{\partial \hat{\psi}_+}{\partial\bar t}=-i 2\bar E \cos(\bar t)\, \frac{\partial \hat{\psi}_+}{\partial \xi} +\left( \xi^2+\bar U\right) \hat{\psi}_+(\xi,\bar t) + \frac1{\sqrt{2\pi}} \psi_{\bar x,0}(\bar t)+i\xi \frac1{\sqrt{2\pi}} \psi_0(\bar t) $$
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Solving for $\hat\psi_+(\xi,\bar t)$ and inverting the Fourier transforms, we obtain
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\begin{equation}\begin{array}{>\displaystyle c}\label{calcpsip}
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\psi_+(\bar x,\bar t)=h_+(\bar x,\bar t)+\\
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\frac1{{2\pi}} {\rm e}^{2i\bar E \bar x\sin(\bar t)}\int_{-\infty}^{\infty} du\,{\rm e}^{i\bar xu-\Phi(u,\bar t)} \int_0^{\bar t} \, {\rm e}^{\Phi(u,\bar s)}\left[ -i \psi_{\bar x,0}(\bar s)+2\bar E\sin\bar s\, \psi_0(\bar s)\right]\, d\bar s\\
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+ \frac1{{2\pi}} {\rm e}^{2i\bar E \bar x\sin(\bar t)}\int_{-\infty}^{\infty} du\,{\rm e}^{i\bar xu-\Phi(u,\bar t)} \int_0^{\bar t} \, {\rm e}^{\Phi(u,\bar s)}\,u\, \psi_0(\bar s)d\bar s
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\end{array}\end{equation}
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where
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\begin{equation}\begin{array}{>\displaystyle c}
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\Phi(u,\bar t)=i\left[ (u^2 +\bar U+2\bar E^2)\bar t - 4\bar E u \cos(\bar t) -\bar E^2 \sin(2\bar t) \right], \\
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h_+(\bar x,\bar t)=\frac 1{2\sqrt{i \pi }}{\rm e }^{2i\bar x\bar E\sin(\bar t)-i(\bar U+2\bar E^2)\bar t+i\bar E^2\sin2\bar t}\int_0^{\infty }d\bar y\, f(\bar y)\, \frac 1{\sqrt{\bar t}}\,{\rm e}^{\frac{i(\bar x-\bar y-4\bar E+4\bar E\cos(\bar t))^2}{4\bar t}}
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\end{array}\end{equation}
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\bigskip
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\indent Taking now the limit $\bar x\to0$ from left and right in (\ref{psiminus}) and in (\ref{calcpsip}) and setting $\psi_-(0,\bar t)=\psi_+(0,\bar t)$, and similarly for $\partial_{\bar x}\psi_\pm $ we obtain (in fact $\psi_-(0,\bar t)=\psi_0(\bar t)=\psi_+(0,\bar t)$ implies that $\partial_{\bar x}\psi_-(0,\bar t)=\partial_{\bar x}\psi_+(0,\bar t)$) one equation with the only unknown function $\psi_0(\bar t)$, which has to satisfy the integral equation
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\begin{equation}\begin{array}{>\displaystyle c}\label{eqcontr}
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\psi_0(\bar t)= h_+(0,\bar t)+ h_-(0,\bar t) -\frac{1}{\pi}\int_0^{\bar t}\left( \int_0^{\bar s} \frac{h_-(0,\bar s')}{\sqrt{\bar s-\bar s'}}\, d\bar s'\right) \, G_1(\bar s,\bar t)\,d\bar s\\
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+\frac{1}{2\pi}\int_0^{\bar t} \left( \int_0^{\bar s} \frac{\psi_0(\bar s')}{\sqrt{\bar s-\bar s'}}\, d\bar s'\right) \, G_1(\bar s,\bar t)\, d\bar s \\
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+\frac{\bar E}{\sqrt{i\pi}}\int_0^{\bar t} d\bar s \, \,\psi_0(\bar s)\, \frac 1{\sqrt{\bar t-\bar s}}\, \left( \sin\bar s\, + \frac{ \cos(\bar t)- \cos(\bar s)}{\bar t-\bar s}\right) \,{\rm e}^{iF_0(\bar s,\bar t)}
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\end{array}\end{equation}
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where
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$$G_1(\bar s,\bar t)=\frac d{d\bar s}\frac{e^{iF_0(\bar s,\bar t)}-1}{\sqrt{\bar t-\bar s}}$$
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with
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\begin{equation}\label{Fzero}
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F_0(s,\bar t)=\frac{4\bar E^2 (\cos(\bar t)- \cos(\bar s))^2}{\bar t-\bar s} -(\bar U_2+2\bar E^2)(\bar t-\bar s) +\bar E^2(\sin 2\bar t-\sin 2\bar s)
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\end{equation}
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We then prove that the integral equation (\ref{eqcontr}) has a unique solution, which implies that (\ref{eq12}) does as well.
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\bigskip
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\indent Setting the initial condition $f(\bar x)=\varphi_1(\bar x)$ (obtained from (\ref{initial}) after the rescaling (\ref{rescale}))
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we obtain explicit functions in equation (\ref{eqcontr}) for $\psi_0(\bar t)$,
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\begin{equation}\label{hminspec}
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h_-(0,\bar t)= {{\rm e}^{-i{\bar k}^{2}\bar t}}\,\frac12\, \left[ 1+{\rm erf} \left( -i^{3/2}\bar k\sqrt {\bar t}\right) \right]
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-R_0\, {{\rm e}^{-i{k}^{2}\bar t}}\,\frac12\, \left[ -1+{\rm erf} \left( -i^{3/2} \bar k\sqrt {\bar t}\right) \right]
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\end{equation}
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and
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\begin{equation}\begin{array}{>\displaystyle c}\label{hpluspec}
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h_+(0,\bar t)= T_0\,\exp[{-i(\bar U+2\bar E^2)\bar t+i\bar E^2\sin 2\bar t-4\,\bar E \alpha\,\cos\bar t +i{\alpha}^{2}\bar t+4\,\bar E \alpha}] \times \\
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\frac 1{2} \left[1- {\rm erf} \left(2\,i^{3/2}\bar E\frac{\cos\bar t-1}{\sqrt {\bar t}}+ \alpha \sqrt{i\bar t} \right) \right]
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\end{array}\end{equation}
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where
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$$\bar k=k/\sqrt{2\omega},\ \ \ \alpha=\sqrt{\bar U-\bar k^2},\ \ \ 1+R_0=T_0=\frac{2i\bar k}{i\bar k-\sqrt{\bar U-\bar k^2}}.$$
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\section{Short time behavior: approach to the stationary state}\label{Sec3}
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\indent We carried out numerical solution of (\ref{eqcontr}) using (\ref{hminspec}) and (\ref{hpluspec}) for a variety of values of $E$.
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To compare with the work in \cite{YGR11}, we take $\frac {\hbar^2k^2}{2m}=\mathcal E_F=4.5$\,eV, $W=5.5$\,eV.
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Unless otherwise specified, we also take $\omega=1.55\ \mathrm{eV}$.
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The laser period $\tau=\frac{2\pi}\omega$ is then equal to $2.7\ \mathrm{fs}$.
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\bigskip
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||||
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||||
\indent The details of the numerical algorithms, which take into account the singular behavior of $\psi(x,t)$ at $x=0$ and $t=0$, will be given in a separate publication.
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\bigskip
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||||
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||||
\indent Figure \ref{fig:wavefunction} shows the real and imaginary parts of $e^{i\frac{k^2}2t}\psi_0(t)$, as well as $|\psi_0(t)|^2$ and the normalized current $\frac1kj(0,t)$.
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||||
While $|\psi_0|^2$ seems more in phase with the real part of$e^{i\frac{k^2}2t}\psi_0$, the current looks more in phase with the imaginary part.
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||||
Figure \ref{fig:current} shows the values of the current $j(0,t)$ passing through the origin as a function of time for different strengths of the field, all at $\omega=1.55$\, eV.
|
||||
We see there a change of behavior as $E$ increases from $E=1$\,V/nm to $E=30$\,V/nm (the Keldysh parameter $\gamma=\frac{2\omega}E\sqrt W$ goes from 18.6 to 0.62).
|
||||
For large values of $E$, fast oscillations appear, which become faster and larger as $E$ grows.
|
||||
The oscillatory behavior within one period for strong fields is also observed in the approximate solution \cite{YGR11}, though the details vary.
|
||||
We have no simple physical explanation for these fast oscillations.
|
||||
They do not fit in with the ``simple three step'' scenario \cite{KSK92,Co93,KLe18}.
|
||||
We note that the height of the first maximum is linear in $E$, while its location is almost independent of $E$.
|
||||
\bigskip
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=8cm]{real.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{imag.pdf}
|
||||
\par\penalty10000\bigskip\penalty10000
|
||||
\includegraphics[width=8cm]{density.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{current.pdf}
|
||||
\caption{
|
||||
The real (a) and imaginary (b) parts of $e^{i\frac{k^2}2t}\psi_0(t)$ the density (c) and the current (d) as a function of $\frac{t\omega}{2\pi}$ for 3 periods, with $E=15\ \mathrm V\cdot\mathrm{nm}^{-1}$, $\omega=1.55\ \mathrm{eV}$.
|
||||
The dotted line represents the phase of the field: $\cos(\omega t)$.
|
||||
}
|
||||
\label{fig:wavefunction}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=8cm]{current01.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{current05.pdf}
|
||||
\par\penalty10000\bigskip\penalty10000
|
||||
\includegraphics[width=8cm]{current18.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{current30.pdf}
|
||||
\caption{
|
||||
The normalized current $\frac jk$ as a function of $\frac{t\omega}{2\pi}$ for $\omega=1.55\ \mathrm{eV}$ and various values of the electric field: $E=1,\ 5,\ 18.6,\ 30\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
The Keldysh parameter $\gamma=\frac{2\omega}E\sqrt W$ for these fields is, respectively, $18.6$, $3.73$, $1.00$ and $0.621$.
|
||||
The dotted line represents the phase of the electric field: $\cos(\omega t)$.
|
||||
As the field increases, fast oscillations in the current appear.
|
||||
These fast oscillations mostly occur while the field is increasing.
|
||||
}
|
||||
\label{fig:current}
|
||||
\end{figure}
|
||||
|
||||
\indent In Figure \ref{fig:cn}, we show a comparison of our solution with the results obtained from a direct solution of (\ref{schrodinger}) via the Crank-Nicolson algorithm.
|
||||
The agreement, especially for the location of the maxima and minima after very early times is very good.
|
||||
At short times, however, the agreement is not so good.
|
||||
This is expected since the Crank-Nicolson scheme is based on approximating derivatives by finite differences.
|
||||
However, at short times, $\psi(0,t)\sim t^{\frac32}$, which has a singular second derivative at $0$, so $\partial_t\psi$ is poorly approximated at short times by finite differences.
|
||||
Note, also, that the Crank-Nicolson method requires a cut-off in $x$, restricting $\psi(x,t)$ to $x\in[-a,a]$.
|
||||
This causes distortions in $\psi$ due to reflections from these artificial boundaries, and so can only be used for short times (this can be avoided by using non-local boundary conditions, such as ``transparent boundary conditions'').
|
||||
\bigskip
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=8cm]{cn.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{cn_short.pdf}
|
||||
\caption{
|
||||
The current computed with our method (blue, color online), compared with the Crank-Nicolson algorithm (red), for $\omega=1.55\ \mathrm{eV}$ and $E=15\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
The maxima and minima seem to occur at the same time, and the agreement is somewhat good for $t>\frac\pi\omega$.
|
||||
The graph on the right focuses on short times, for which the Crank-Nicolson algorithm produces a different, and quite surprising result: the current initially shoots down to negative values before rising back up, but the field is initially positive, which should drive the current up, not down.
|
||||
The discrepancy is due to the fact that the wavefunction is singular at $t=0$ (it has a divergent second derivative), and that the Crank-Nicolson algorithm approximates derivatives using finite differences, which is good only for regular functions.
|
||||
}
|
||||
\label{fig:cn}
|
||||
\end{figure}
|
||||
|
||||
\indent Also shown in the figures is the running average of the current
|
||||
\begin{equation}
|
||||
\left<j\right>_t:=\frac1\tau\int_{t-\tau}^t j(0,t)
|
||||
,\quad
|
||||
\tau:=\frac{2\pi}\omega
|
||||
.
|
||||
\end{equation}
|
||||
It is seen there that while the current appears to approach its long time value rather rapidly it does not do so fully until much later.
|
||||
As seen in Figure \ref{fig:avgcurrent}, where we plot $\left<j\right>$ for $\omega=6\ \mathrm{eV}$, $E=10\ \mathrm{V}\cdot\mathrm{nm}^{-1}$, $\gamma=9.6$, $\left<j\right>_t$ is still not all that close to its asymptotic value even when $t\approx48\tau$.
|
||||
\bigskip
|
||||
|
||||
\indent The rate of the decay of the average current to its asymptotic value is evaluated in Figure \ref{fig:decay}.
|
||||
In order to compute this rate without having to guess the asymptotic value, we proceed as follows.
|
||||
At the end of every laser period $t_n=\frac{2\pi}\omega n$, we compute the minimal value $\mu_n$ and maximal value $M_n$ of the average current in the period $(\frac{2\pi}\omega(n-1),\frac{2\pi}\omega n]$.
|
||||
The plot shoes $M_n-\mu_n$ as a function of $t$, and shows that $\left<j\right>_t\approx\left<j\right>_\infty+g(t)t^{-\frac32}$, where $g(t)$ is bounded and asymptotically constant.
|
||||
\bigskip
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=8cm]{avgcurrent.pdf}
|
||||
\hfill
|
||||
\includegraphics[width=8cm]{avgcurrent_zoom.pdf}
|
||||
\caption{
|
||||
The normalized average current $\frac1k\left<j\right>_t$ as a function if $\frac{t\omega}{2\pi}$ for $\omega=6\ \mathrm{eV}$ and $E=10\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
The two plots show the same data, but the first one focuses on times between the 12th and 48th period.
|
||||
Here, $\omega$ is large enough that absorbing one photon suffices to overcome the work function.
|
||||
Even after 48 periods, the average current has not converged to its asymptotic value.
|
||||
}
|
||||
\label{fig:avgcurrent}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\hfil\includegraphics[width=8cm]{decay.pdf}
|
||||
\caption{
|
||||
The convergence rate to the asymptote of the average current as a function of $\frac{t\omega}{2\pi}$ on a log-log plot for $\omega=6$ and $E=10\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
The dots are computed at the end of each period $t_n=\frac{2\pi}\omega n$, and their value is the difference between the maximun $M_t$ and the minimum $\mu_t$ of the normalized average current $\frac1k\left<j\right>_t$ in the period immediately preceding $t_n$.
|
||||
The red line is a plot of $0.0030\times(\frac{t\omega}{2\pi})^{-\frac32}$, which fits the data rather well.
|
||||
}
|
||||
\label{fig:decay}
|
||||
\end{figure}
|
||||
|
||||
\indent In Figure \ref{fig:omega}, we show an estimate of the asymptotic average current as a function of $\omega$ in the vicinity of the one-photon threshold $\omega_c=W$ for $E=10\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
As we argued above, the average current converges slowly to its asymptotic value.
|
||||
In order to estimate this asymptotic value without computing the current at very large times, we actually compute the average of the average current over a laser period:
|
||||
\begin{equation}
|
||||
\left<\left<j\right>\right>:=\frac1\tau\int_{T-\tau}^T dt\ \left<j\right>_t
|
||||
.
|
||||
\end{equation}
|
||||
We see that there is a steep increase in $\left<\left<j\right>\right>$ as $\omega$ increases past $\omega_c$.
|
||||
This is precisely what is observed in experiments on the photoelectric effect, where the emission of electrons from the metal surface has such a threshold \cite{Mi16}.
|
||||
This became a key element in Einstein's ansatz of localized photons.
|
||||
Here, in the semi-classical treatment of the laser field, this phenomenon appears as a resonance.
|
||||
The ponderomotive term $\frac{E^2}{4\omega^2}$, which appears in the photon energy, see below, is negligible compared to the work function $W$.
|
||||
\bigskip
|
||||
|
||||
\begin{figure}
|
||||
\hfil\includegraphics[width=8cm]{omega.pdf}
|
||||
\caption{
|
||||
The average of the average of the normalized current $\frac1k\left<\left<j\right>_t\right>$ after 12 periods as a function of $\omega$, for $E=10\ \mathrm{V}\cdot\mathrm{nm}^{-1}$.
|
||||
After 12 periods, the average current $\left<j\right>_t$ is still fluctuating quite a lot, so, in order to eliminate these fluctuations and get closer to the asymptotic value $\left<j\right>_\infty$, we average the average current over a laser period.
|
||||
}
|
||||
\label{fig:omega}
|
||||
\end{figure}
|
||||
|
||||
\section{Long time behavior of $\psi(x,t)$}\label{longtime}
|
||||
\indent The long time behavior of the system is given by the poles of the Laplace transform
|
||||
$$\hat{\psi}(x,p)=\int_0^{\infty}{\rm e}^{-pt} \psi(x,t)\, dt$$
|
||||
on the imaginary axis, as can be seen by taking the inverse Laplace transform
|
||||
\begin{equation}
|
||||
\psi(x,t)=\int_{-i\infty}^{i\infty}dp\ e^{pt}\hat\psi(x,p)
|
||||
.
|
||||
\end{equation}
|
||||
Other poles, which necessarily have negative real parts, give rise to exponentially decaying terms while branch cuts generally contribute $t^{-\frac32}$ terms to the approach to the asymptotic state.
|
||||
As mentioned earlier, the time asymptotic of $\psi$ is of the form
|
||||
\begin{equation}\label{4p1}
|
||||
\psi(x,t)\sim {\rm e}^{\frac 12 i k^2 t} \bar{\psi}(x,t)
|
||||
\end{equation}
|
||||
where $\bar{\psi}(x,t)$ is periodic in $t$ with period $2\pi/\omega$ and $\frac 12 k^2$ is the energy of the electrons in the incoming beam.
|
||||
This corresponds to the poles of $\hat{\psi}(p,t)$ on the imaginary axis being at
|
||||
\begin{equation}\label{4p2}
|
||||
p=-\frac 12 i k^2+i\omega n,\ \ \ n\mathrm{\ \ integer}
|
||||
\end{equation}
|
||||
\bigskip
|
||||
|
||||
\indent We further show that $\bar{\psi}(x,t)$ coincides, after the change of gauge, with the wave function $\mathcal{U}(x,t)$ computed by Faisal et al \cite{FKS05}.
|
||||
In that work it was assumed (\ref{schrodinger}) (in the magnetic gauge) has a solution of the form (\ref{4p1}) with an incoming beam $e^{ikx}$ for $x<0$, without considering any initial conditions.
|
||||
Computing the residues at the poles on the imaginary axis we show that
|
||||
\begin{equation}\label{4p3}
|
||||
\bar\psi(x,t)\sim \left\{\begin{array}{>\displaystyle ll}
|
||||
e^{ikx}
|
||||
+\sum_{m\in\mathbb Z}e^{-im\omega t}e^{-ix\sqrt{k^2+2m\omega}}\mathcal R_m
|
||||
&\mathrm{for\ }x<0
|
||||
\\[0.5cm]
|
||||
e^{i\frac E\omega x\sin\omega t}\sum_{n,m\in\mathbb Z}e^{-in\omega t}g_{n-m}^{(\kappa_m)}e^{-\kappa_mx}\mathcal T_m
|
||||
&\mathrm{for\ }x>0
|
||||
\end{array}\right.
|
||||
\end{equation}
|
||||
where
|
||||
\begin{equation}
|
||||
\kappa_m=\sqrt{2U-k^2+\frac{E^2}{2\omega^2}-2m\omega}
|
||||
\label{kappa}
|
||||
\end{equation}
|
||||
and
|
||||
\begin{equation}
|
||||
g_{n-m}^{(\kappa_m)}=\frac\omega{2\pi}\int_0^{\frac{2\pi}\omega}dt\ e^{-i(n-m)\omega t}e^{\frac{i\frac{E^2}{4\omega^2}}\omega\sin(2\omega t)+\kappa_m\frac{2E}{\omega^2}\cos(\omega t)}
|
||||
.
|
||||
\end{equation}
|
||||
This is exactly of the form considered in \cite{FKS05}.
|
||||
$\mathcal R_n$ and $\mathcal T_m$ are computed by matching boundary values of $\psi(0,t)$ and $\psi_{x,0}(t)$ at $x=0$.
|
||||
\bigskip
|
||||
|
||||
\indent A physical interpretation of (\ref{4p3}), see \cite{FKS05}, is that an electron in a beam coming from $-\infty$ and moving in the positive $x$-direction, ${\rm e}^{ikx},\ k>0$, absorbs or emits ``$m$ photons'' and is either reflected, transmitted or damped.
|
||||
Transmission occurs when $m\omega>U+\frac {E^2}{4\omega^2}-\frac{k^2}2\equiv\omega_c$.
|
||||
The $\frac{E^2}{4\omega^2}$ in (\ref{kappa}) corresponds to the ponderomotive energy of the electron in the laser field.
|
||||
Damping occurs when the inequalities are in the opposite direction.
|
||||
$\omega_c$ is the minimum frequency necessary to push the electron with kinetic energy $\frac12k^2$ (in the $x$-direction) over the potential barrier of height $U-\frac12k^2=W$.
|
||||
For $x\gg0$, the current in the $m$-photon channel will have kinetic energy $m\omega-\omega_c$ and the current will be given by $\sqrt{m\omega-\omega_c}$.
|
||||
This will also be equal to the average current at large $t$, which is independent of $x$.
|
||||
This explains the picture in Figure 4 for $m=1$.
|
||||
The larger $m$ values necessary for smaller $\omega$ are difficult to see.
|
||||
\bigskip
|
||||
|
||||
\indent The asymptotic form (\ref{4p3}) is true for all initial conditions of the form $\Theta(-x)e^{ikx}+f_0(s)$ as long as $f_0(x)$ only contains terms which are square integrable.
|
||||
The additional terms in $\psi(x,t)$ which come from $f_0(x)$ go to zero as $t\to\infty$.
|
||||
This follows from the fact, proven in \cite{CCe}, that the Floquet operator associated to (\ref{schrodinger}) has no point spectrum.
|
||||
\bigskip
|
||||
|
||||
|
||||
|
||||
\vfill
|
||||
|
||||
\delimtitle{\bf Acknowledgements}
|
||||
We thank David Huse, Kevin Jensen and Donald Schiffler for very valuable discussions. This work was supported by AFOSR Grant No. FA9500-16-1-0037. O.C. was partially supported by the NSF-DMS (Grant No. 1515755). I.J. was partially supported by the NSF-DMS (Grants No. 31128155 and 1802170). J.L.L. thanks the Institute for Advanced Study for its hospitality.
|
||||
\enddelim
|
||||
|
||||
\eject
|
||||
|
||||
\begin{thebibliography}{WWW99}
|
||||
\small
|
||||
\IfFileExists{bibliography/bibliography.tex}{\input bibliography/bibliography.tex}{}
|
||||
\end{thebibliography}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
55
Makefile
Normal file
55
Makefile
Normal file
@ -0,0 +1,55 @@
|
||||
PROJECTNAME=$(basename $(wildcard *.tex))
|
||||
LIBS=$(notdir $(wildcard libs/*))
|
||||
FIGS=$(notdir $(wildcard figs/*.fig))
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
|
||||
|
||||
all: $(PROJECTNAME)
|
||||
|
||||
$(PROJECTNAME): $(LIBS) $(FIGS)
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -synctex=1 $@.tex
|
||||
|
||||
$(PROJECTNAME).aux: $(LIBS) $(FIGS)
|
||||
pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
|
||||
|
||||
|
||||
$(SYNCTEXS): $(LIBS) $(FIGS)
|
||||
pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
|
||||
|
||||
|
||||
libs: $(LIBS)
|
||||
|
||||
$(LIBS):
|
||||
ln -fs libs/$@ ./
|
||||
|
||||
figs: $(FIGS)
|
||||
|
||||
$(FIGS):
|
||||
make -C figs/$@
|
||||
for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
|
||||
|
||||
|
||||
clean-aux: clean-figs-aux
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .out, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .toc, $(PROJECTNAME))
|
||||
|
||||
clean-libs:
|
||||
rm -f $(LIBS)
|
||||
|
||||
clean-figs:
|
||||
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; )
|
||||
rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
|
||||
|
||||
clean-figs-aux:
|
||||
$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
|
||||
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS) $(SYNCTEXS)
|
||||
|
||||
clean: clean-aux clean-tex clean-libs clean-figs
|
||||
43
README
Normal file
43
README
Normal file
@ -0,0 +1,43 @@
|
||||
This directory contains the source files to typeset the article, and generate
|
||||
the figures. This can be accomplished by running
|
||||
make
|
||||
|
||||
This document uses a custom class file, located in the 'libs' directory, which
|
||||
defines a number of commands. Most of these are drop-in replacements for those
|
||||
defined in the 'article' class.
|
||||
|
||||
Some extra functionality is provided in custom style files, located in the
|
||||
'libs' directory.
|
||||
|
||||
The figures are generated from data computed using the 'photocomp' tool, which
|
||||
has not been released yet, so the data for the figures is provided here.
|
||||
|
||||
|
||||
|
||||
* Dependencies:
|
||||
|
||||
pdflatex
|
||||
TeXlive packages:
|
||||
amsfonts
|
||||
array
|
||||
color
|
||||
graphics
|
||||
hyperref
|
||||
latex
|
||||
marginnote
|
||||
pgf
|
||||
standalone
|
||||
GNU make
|
||||
gnuplot
|
||||
|
||||
* Files:
|
||||
|
||||
Costin_Costin_Jauslin_Lebowitz_2019.tex:
|
||||
main LaTeX file
|
||||
|
||||
libs:
|
||||
custom LaTeX class file
|
||||
|
||||
figs:
|
||||
source code for the figures
|
||||
|
||||
46
bibliography/bibliography.tex
Normal file
46
bibliography/bibliography.tex
Normal file
@ -0,0 +1,46 @@
|
||||
\bibitem[Co93]{Co93}P.B. Corkum - {\it Plasma perspective on strong field multiphoton ionization}, Physical Review Letters, volume\-~71, issue\-~13, pages\-~1994-1997, 1993,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.71.1994}{10.1103/PhysRevLett.71.1994}}.\par\medskip
|
||||
|
||||
\bibitem[CCe]{CCe}O. Costin, R. Costin, I. Jauslin, J.L. Lebowitz, {\it in preparation}.\par\medskip
|
||||
|
||||
\bibitem[CCe18]{CCe18}O. Costin, R. Costin, I. Jauslin, J.L. Lebowitz - {\it Solution of the time dependent Schr\"odinger equation leading to Fowler-Nordheim field emission}, Journal of Applied Physics, volume\-~124, number\-~213104, 2018,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1063/1.5066240}{10.1063/1.5066240}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1808.00936}{1808.00936}}.\par\medskip
|
||||
|
||||
\bibitem[CN47]{CN47}J. Crank, P. Nicolson - {\it A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type}, Mathematical Proceedings of the Cambridge Philosophical Society, volume\-~43, issue\-~1, pages\-~50-67, 1947,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1017/S0305004100023197}{10.1017/S0305004100023197}}.\par\medskip
|
||||
|
||||
\bibitem[FKS05]{FKS05}F.H.M. Faisal, J.Z. Kami\'nski, E. Saczuk - {\it Photoemission and high-order harmonic generation from solid surfaces in intense laser fields}, Physical Review A, volume\-~72, issue\-~2, number\-~023412, 2005,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevA.72.023412}{10.1103/PhysRevA.72.023412}}.\par\medskip
|
||||
|
||||
\bibitem[Fo97]{Fo97}A.S. Fokas - {\it A unified transform method for solving linear and certain nonlinear PDEs}, Proceedings of the Royal Society of London A, volume\-~453, issue\-~1962, pages\-~1411-1443, 1997,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1098/rspa.1997.0077}{10.1098/rspa.1997.0077}}.\par\medskip
|
||||
|
||||
\bibitem[Fo16]{Fo16}R.G. Forbes - {\it Field Electron Emission Theory}, Proceedings of Young Researchers in Vacuum Micro/Nano Electronics, IEEE, 2016,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1109/VMNEYR.2016.7880403}{10.1109/VMNEYR.2016.7880403}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1801.08251}{1801.08251}}.\par\medskip
|
||||
|
||||
\bibitem[FN28]{FN28}R.H. Fowler, L. Nordheim - {\it Electron emission in intense electric fields}, Proceedings of the Royal Society of London A, volume\-~119, issue\-~781, pages\-~173-181, 1928,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1098/rspa.1928.0091}{10.1098/rspa.1928.0091}}.\par\medskip
|
||||
|
||||
\bibitem[Je17]{Je17}K.L. Jensen - {\it Introduction to the Physics of Electron Emission}, Wiley, 2017.\par\medskip
|
||||
|
||||
\bibitem[KSK92]{KSK92}J.L. Krause, K.J. Schafer, K.C. Kulander - {\it High-order harmonic generation from atoms and ions in the high intensity regime}, Physical Review Letters, volume\-~68, issue\-~24, pages\-~3535-3538, 1992,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.68.3535}{10.1103/PhysRevLett.68.3535}}.\par\medskip
|
||||
|
||||
\bibitem[KSH11]{KSH11}M. Kr\"uger, M. Schenk, P. Hommelhoff - {\it Attosecond control of electrons emitted from a nanoscale metal tip}, Nature, volume\-~475, issue\-~7354, pages\-~78-81, 2011,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1038/nature10196}{10.1038/nature10196}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1107.1591}{1107.1591}}.\par\medskip
|
||||
|
||||
\bibitem[KLe18]{KLe18}M. Kr\"uger, C. Lemell, G. Wachter, J. Burgdörfer, P. Hommelhoff - {\it Attosecond physics phenomena at nanometric tips}, Journal of Physics B: Atomic, Molecular and Optical Physics, volume\-~51, issue\-~17, number\-~172001, 2018,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1088/1361-6455/aac6ac}{10.1088/1361-6455/aac6ac}}.\par\medskip
|
||||
|
||||
\bibitem[Mi16]{Mi16}R.A. Millikan - {\it A Direct Photoelectric Determination of Planck's $h$}, Physical Review, volume\-~7, issue\-~3, pages\-~355-388, 1916,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.7.355}{10.1103/PhysRev.7.355}}.\par\medskip
|
||||
|
||||
\bibitem[Ry18]{Ry18}Y. Rybalko - {\it Initial value problem for the time-dependent linear Schrodinger equation with a point singular potential by the unified transform method}, Opuscula Mathematica, volume\-~38, number\-~6, pages\-~883-898, 2018,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.7494/OpMath.2018.38.6.883}{10.7494/OpMath.2018.38.6.883}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1601.08008}{1601.08008}}.\par\medskip
|
||||
|
||||
\bibitem[YGR11]{YGR11}S.V. Yalunin, M. Gulde, C. Ropers - {\it Strong-field photoemission from surfaces: Theoretical approaches}, Physical Review B, volume\-~84, issue\-~19, number\-~195426, 2011,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevB.84.195426}{10.1103/PhysRevB.84.195426}}.\par\medskip
|
||||
|
||||
\bibitem[ZL16]{ZL16}P. Zhang, Y.Y. Lau - {\it Ultrafast strong-field photoelectron emission from biased metal surfaces: exact solution to time-dependent Schr\"odinger Equation}, Scientific Reports, volume\-~6, number\-~19894, 2016,\par\penalty10000
|
||||
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1038/srep19894}{10.1038/srep19894}}.\par\medskip
|
||||
|
||||
39
figs/avgcurrent.fig/Makefile
Normal file
39
figs/avgcurrent.fig/Makefile
Normal file
@ -0,0 +1,39 @@
|
||||
PROJECTNAME=avgcurrent avgcurrent_zoom decay
|
||||
|
||||
PHOTOCOMP_PATH=
|
||||
|
||||
DATS=avgcurrent.dat decay.dat
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(DATS)
|
||||
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
avgcurrent.dat: save.dat
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=6;n_periods=48;J=480;E=10e9" mc -s save.dat > $@
|
||||
|
||||
decay.dat: save.dat
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=6;n_periods=48;J=480;E=10e9" mc_decay -s save.dat > $@
|
||||
|
||||
save.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=6;n_periods=48;J=480;E=10e9" save > $@
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-dat:
|
||||
rm -f $(DATS) save.dat
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
|
||||
clean: clean-aux clean-tex
|
||||
9606
figs/avgcurrent.fig/avgcurrent.dat
Normal file
9606
figs/avgcurrent.fig/avgcurrent.dat
Normal file
File diff suppressed because it is too large
Load Diff
24
figs/avgcurrent.fig/avgcurrent.gnuplot
Normal file
24
figs/avgcurrent.fig/avgcurrent.gnuplot
Normal file
@ -0,0 +1,24 @@
|
||||
set ylabel "$\\frac1k\\left<j\\right>_t$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,12
|
||||
set ytics 0,0.001
|
||||
|
||||
set xrange [0:48]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot "avgcurrent.dat" using 1:($1>1 ? $6 : 1/0) with lines linestyle 1
|
||||
25
figs/avgcurrent.fig/avgcurrent_zoom.gnuplot
Normal file
25
figs/avgcurrent.fig/avgcurrent_zoom.gnuplot
Normal file
@ -0,0 +1,25 @@
|
||||
set ylabel "$\\frac1k\\left<j\\right>_t$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,12
|
||||
set ytics 0.00130,0.00004
|
||||
|
||||
set yrange [0.00128:0.00138]
|
||||
set xrange [12:48]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot "avgcurrent.dat" using 1:6 with lines linestyle 1
|
||||
53
figs/avgcurrent.fig/decay.dat
Normal file
53
figs/avgcurrent.fig/decay.dat
Normal file
@ -0,0 +1,53 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=6.000000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=0.934268975891369, E=1.000000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=7.266837529084202e-02 omega=6.000000000000000e-01 m=1.000000000000000e+00, keldysh=7.216404962767393e+00
|
||||
#numerical precision (matching): n_periods=48 NC=12 gl_order=16 J0=1 J=480
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
# t mu_t M_t
|
||||
2.005000000000000e+00 -4.465249574292407e-05 2.892008997946130e-03
|
||||
3.004999999999999e+00 6.806473586532007e-04 1.611344559925361e-03
|
||||
4.004999999999997e+00 9.531666802876900e-04 1.430074084610480e-03
|
||||
5.004999999999996e+00 1.112095215394091e-03 1.415755296437017e-03
|
||||
6.004999999999995e+00 1.178723364609898e-03 1.434548730775139e-03
|
||||
7.004999999999999e+00 1.230653978557152e-03 1.451154221498075e-03
|
||||
8.000000000000005e+00 1.284082546921191e-03 1.456183724818763e-03
|
||||
9.000000000000011e+00 1.320101942418750e-03 1.449409650442600e-03
|
||||
1.000000000000002e+01 1.332128084560356e-03 1.433544083730075e-03
|
||||
1.100000000000002e+01 1.328615144193408e-03 1.411834798831924e-03
|
||||
1.200000000000003e+01 1.317802662449091e-03 1.388121233446665e-03
|
||||
1.300000000000003e+01 1.305974610489081e-03 1.375961738972150e-03
|
||||
1.400000000000004e+01 1.297012109589079e-03 1.364747654234101e-03
|
||||
1.500000000000004e+01 1.292775935877827e-03 1.351347207493206e-03
|
||||
1.600000000000005e+01 1.293822677757008e-03 1.343607304368543e-03
|
||||
1.700000000000005e+01 1.299820410514768e-03 1.342878973466090e-03
|
||||
1.800000000000006e+01 1.309385031252287e-03 1.347024476018631e-03
|
||||
1.900000000000006e+01 1.320173072770978e-03 1.353534908845761e-03
|
||||
2.000000000000007e+01 1.324465132367436e-03 1.360198367149491e-03
|
||||
2.100000000000008e+01 1.330100620972184e-03 1.365310202042966e-03
|
||||
2.200000000000008e+01 1.336044821630408e-03 1.367671972762798e-03
|
||||
2.300000000000009e+01 1.338710049596377e-03 1.366696969752792e-03
|
||||
2.400000000000009e+01 1.337973002387375e-03 1.362663493743734e-03
|
||||
2.500000000000009e+01 1.334759175167112e-03 1.356744645818275e-03
|
||||
2.600000000000006e+01 1.330279210201444e-03 1.350842056746174e-03
|
||||
2.700000000000004e+01 1.325840812522160e-03 1.348671983114142e-03
|
||||
2.800000000000002e+01 1.322654598995199e-03 1.345258918518337e-03
|
||||
2.900500000000000e+01 1.321582620668878e-03 1.341996494328002e-03
|
||||
3.000499999999998e+01 1.322844314348249e-03 1.340940035684045e-03
|
||||
3.100499999999995e+01 1.325948216456572e-03 1.342052212740544e-03
|
||||
3.200499999999993e+01 1.329986989195847e-03 1.344786288894575e-03
|
||||
3.300499999999991e+01 1.333421117850701e-03 1.348239586830857e-03
|
||||
3.400499999999989e+01 1.334922273485275e-03 1.351365520831539e-03
|
||||
3.500499999999987e+01 1.337371756144218e-03 1.353285967255712e-03
|
||||
3.600499999999985e+01 1.339340919372187e-03 1.353558131763480e-03
|
||||
3.700499999999982e+01 1.339607534213708e-03 1.352269215976699e-03
|
||||
3.800499999999980e+01 1.338259311876398e-03 1.349860941552041e-03
|
||||
3.900499999999978e+01 1.335843353599698e-03 1.346881687730867e-03
|
||||
4.000499999999976e+01 1.333173924311831e-03 1.344961245451776e-03
|
||||
4.100499999999974e+01 1.331033693671063e-03 1.343619013767633e-03
|
||||
4.200499999999972e+01 1.329937987977380e-03 1.341614035795568e-03
|
||||
4.300499999999970e+01 1.330038327956477e-03 1.340500676012152e-03
|
||||
4.400499999999968e+01 1.331216650002774e-03 1.340788379664775e-03
|
||||
4.500499999999965e+01 1.333210987171334e-03 1.342234189388972e-03
|
||||
4.600499999999963e+01 1.335622628018670e-03 1.344273805075085e-03
|
||||
4.700499999999961e+01 1.336632341415729e-03 1.346277075142191e-03
|
||||
4.799999999999959e+01 1.337964973402016e-03 1.347746441811054e-03
|
||||
34
figs/avgcurrent.fig/decay.gnuplot
Normal file
34
figs/avgcurrent.fig/decay.gnuplot
Normal file
@ -0,0 +1,34 @@
|
||||
set ylabel offset 5,0 "$M_t-\\mu_t$"
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics add("10" 10, "20" 20, "30" 30, "40" 40)
|
||||
set mxtics 81
|
||||
set ytics add ("$10^{-5}$" 0.00001, "$10^{-4}$" 0.0001)
|
||||
|
||||
set xrange [10:50]
|
||||
set yrange [0.000007:0.00015]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
# logscale
|
||||
set logscale xy
|
||||
|
||||
# fit
|
||||
f(x)=-1.5*x+b
|
||||
|
||||
fit [1:] f(x) "decay.dat" u (log10($1)):(log10($3-$2)) via b
|
||||
|
||||
plot 10**f(log10(x)) linestyle 2, "decay.dat" using 1:($3-$2) with points linestyle 1
|
||||
487
figs/avgcurrent.fig/save.dat
Normal file
487
figs/avgcurrent.fig/save.dat
Normal file
@ -0,0 +1,487 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=6.000000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=0.934268975891369, E=1.000000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=7.266837529084202e-02 omega=6.000000000000000e-01 m=1.000000000000000e+00, keldysh=7.216404962767393e+00
|
||||
#numerical precision (matching): n_periods=48 NC=12 gl_order=16 J0=1 J=480
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
480
|
||||
12 7.055350578843251e-01 -1.118122180108418e+00 -2.640685032764412e-01 -1.553800164380189e-01 -7.304626492933619e-02 -2.573420862470561e-02 -3.786290652531523e-03 7.460077530076078e-03 -2.817454264016051e-04 1.011443432259879e-03 7.164966002685155e-05 6.926345132725265e-05 1.103362165328192e-05 6.706450770592399e-06 1.357417921660424e-06 -2.541372315622481e-07 1.322515969230063e-07 -1.474041749784050e-07 -1.618720930368805e-09 -2.096450428357976e-08 -2.062004079557157e-09 -1.345453464999124e-09 -1.933252177251106e-10 8.395423618461507e-11
|
||||
12 5.684180856850439e-02 -1.325846096618561e+00 -3.103938228247618e-01 -1.762380135648777e-02 -2.190124266969761e-03 1.776370155072481e-02 6.280987360430604e-04 2.176625926765744e-04 1.865387857106299e-05 -1.431702177006529e-05 -3.955534851205918e-07 -1.200091384920538e-06 -3.480261032715016e-08 3.308252167090656e-08 3.232971417401563e-10 -1.789105922861643e-09 -1.687880431742683e-11 2.704418040303960e-10 -1.362215056589008e-13 -3.123815818102854e-11 2.027912417415178e-13 4.188082621388677e-12 -2.031423148324697e-14 -5.479207208579368e-13
|
||||
12 -5.545923812851334e-01 -1.214512273930488e+00 -2.935765491317352e-01 1.294560630166826e-01 6.736144275771588e-03 1.832852380541900e-02 8.201720943406519e-04 -1.668589473178039e-04 2.918459481343491e-06 -3.160926233005151e-05 -1.153721733469597e-06 -5.090556729432279e-07 -2.769605473012455e-08 3.600574055328908e-08 5.107495485881753e-10 1.045894345431582e-09 4.157468681795269e-11 3.097525678508758e-11 2.247076552076040e-12 -1.839560566640043e-12 -1.569092908093244e-14 -6.040755057934095e-14 -3.645573832985973e-15 -4.385058088163153e-15
|
||||
12 -1.057410248734077e+00 -8.216664759493761e-01 -2.014754843015474e-01 2.590628323405498e-01 1.600160355614129e-02 1.313776100338398e-02 6.545672115251774e-04 -6.961280318832333e-04 -2.459535224819033e-05 -3.053710857651208e-05 -1.435200103676440e-06 7.352531419207054e-07 1.435579600431896e-08 6.476230346072252e-08 2.631272385617621e-09 3.515383199142949e-10 6.273228677993138e-11 -9.181459519791227e-11 -2.508649990797931e-12 -4.406619131728543e-12 -2.204297623778083e-13 2.797862949709471e-14 -2.426891701226976e-15 8.934868524050004e-15
|
||||
12 -1.313476173971430e+00 -2.296801328550294e-01 -5.065788910841140e-02 3.240974578758005e-01 2.068337346830100e-02 2.602623043731873e-03 7.758557490688609e-05 -9.868912213781876e-04 -4.329171820512973e-05 -1.732846061333781e-06 -1.240078881320128e-07 1.958302728232457e-06 9.065190183953094e-08 1.624190148482308e-08 1.590606190053160e-09 -4.023456363341748e-09 -1.623264002164702e-10 -1.207397045346800e-10 -7.608105557339286e-12 5.625374050005105e-12 1.443474821930860e-13 4.130875709545263e-13 2.029019041051293e-14 -1.110820141264734e-16
|
||||
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|
||||
12 1.335577434456908e+00 2.266308390710302e-01 4.658120243308320e-02 -3.362583590224377e-01 -2.222720146066859e-02 -1.929985671604436e-03 -1.982258498365220e-05 1.114979773488846e-03 5.131873475450845e-05 -1.031449793859754e-06 9.835027706480664e-08 -2.372119548027188e-06 -1.090267605495372e-07 -2.428135683762366e-08 -2.439487986600744e-09 4.710654555081465e-09 1.799711531036408e-10 1.758582128833538e-10 1.038101371311567e-11 -5.500499330005681e-12 -9.794680458892392e-14 -5.156937036478143e-13 -6.726597608554179e-15 -5.587439200126407e-17
|
||||
12 1.259504815709385e+00 -4.215048513760190e-01 -1.190576835613098e-01 -3.020144338609592e-01 -1.796100906071119e-02 9.824733617112629e-03 6.670793676207738e-04 7.398312643949723e-04 2.615163380835916e-05 -4.161601092633060e-05 -2.420376618706230e-06 -1.056100553249845e-06 -5.797196225849413e-08 1.302468475105818e-07 6.473908964687463e-09 3.711232085412603e-09 2.347508515704621e-10 -2.969926997684847e-10 -1.246399107110689e-11 -1.389606934247295e-11 -7.772105723851760e-13 4.679023697654935e-13 8.754385950512253e-15 3.317021848739632e-14
|
||||
12 9.055465950676899e-01 -9.271243414272130e-01 -2.274384965621559e-01 -1.996441550540613e-01 -9.097651642210844e-03 1.460148302835724e-02 6.925923596228842e-04 8.677942447809084e-05 -1.945010139663927e-05 -2.987094613952051e-05 -1.355651007842801e-06 1.979921150738879e-06 1.332083935415251e-07 6.735958864974339e-08 3.553422207209703e-09 -7.669542954408529e-09 -4.082783336019231e-10 -1.916835543663685e-10 -1.036078227364837e-11 2.072599530210157e-11 1.009779503366434e-12 5.551549174993968e-13 3.424865999924838e-14 -5.340420534646930e-14
|
||||
12 3.998594316056461e-01 -1.209927048572237e+00 -2.731438762830046e-01 -8.359195305132401e-02 -2.960934377046528e-03 1.415758341828494e-02 3.440272071758517e-04 -6.258207719952366e-05 -1.451992448721385e-05 8.034438657490717e-06 1.517421803887260e-06 1.055395444032068e-06 5.368425576265749e-08 -1.170827630612640e-07 -7.255720431759897e-09 -2.125609926932489e-09 -6.179889247251133e-11 4.072533709467732e-10 2.151907868836755e-11 6.144994841984421e-13 -9.971115961770815e-14 -1.080288324688579e-12 -6.136888942817490e-14 1.240907702624671e-14
|
||||
12 -1.582255128092843e-01 -1.264254375821977e+00 -2.818364768056051e-01 2.946242831966276e-02 8.213774498857382e-04 1.438371590700023e-02 3.595650552780121e-04 8.610717153671587e-05 1.374421691689417e-05 2.985215406415780e-06 7.434444601942318e-07 -1.224017672537329e-06 -8.627330926495444e-08 -3.780380152961124e-08 -8.587766956752515e-10 5.253720665705818e-09 2.843545383123034e-10 -3.357309849450619e-11 -5.647204607953696e-12 -1.382038891922883e-11 -6.070089813911554e-13 4.477725791537901e-13 3.030492566074611e-14 1.367064903492572e-14
|
||||
12 -6.987275135003729e-01 -1.087706057372236e+00 -2.538461918286618e-01 1.475198770235239e-01 6.596472983679658e-03 1.485750430070053e-02 5.927187422332467e-04 -6.787836733297696e-05 1.007839435240352e-05 -2.069070119387191e-05 -8.773743805553132e-07 -7.977218571518958e-07 -3.171600922715760e-08 4.946425622531633e-08 2.883659822660918e-09 4.281379521714696e-10 -4.758187052370470e-11 -1.470224090382950e-10 -6.120916394612904e-12 5.282196278706065e-12 3.480256204912169e-13 1.575149890452170e-13 -6.140859716398153e-15 -6.558218428433980e-15
|
||||
12 -1.130166150140907e+00 -6.808993887111535e-01 -1.713673768047091e-01 2.566903996056935e-01 1.402732897984131e-02 1.173261971293249e-02 5.949081554296336e-04 -4.650699253306760e-04 -9.954551055197509e-06 -2.572698456999890e-05 -9.534216874040558e-07 1.953235296306382e-07 1.247913444965985e-08 2.681485305247247e-08 2.420220163070529e-10 -1.053253359423009e-09 -6.177173142760399e-11 3.359818508740409e-11 3.061965291018423e-12 2.399608064598462e-12 4.642653969089372e-14 -1.564480555081435e-13 -1.273667861757232e-14 1.447651078009628e-14
|
||||
12 -1.340875789603667e+00 -9.595478030288788e-02 -3.464448874179577e-02 3.217157348351238e-01 1.963359131568928e-02 3.903449441454900e-03 2.989851100974066e-04 -8.177047146650882e-04 -2.619110555248206e-05 -1.695526513658625e-05 -6.923798882431863e-07 6.461499570546116e-07 8.204948821114435e-09 1.753346276111777e-08 -2.245270682606734e-11 3.486142902038926e-10 3.559277181315283e-11 2.873912875590909e-11 1.627774910181841e-12 -1.860996449671040e-12 -6.760582882225789e-14 -3.716972832408074e-14 3.351142002146304e-17 1.101687398300730e-14
|
||||
12 -1.247407245878053e+00 5.451298631830217e-01 1.286788329618529e-01 3.102333540509445e-01 2.029088638052004e-02 -7.024566277960910e-03 -2.175434944272436e-04 -9.584505164165893e-04 -3.729453896356764e-05 1.202294506930233e-06 -3.393278949731234e-07 1.215714502604137e-06 2.844390661984888e-08 2.809032810960098e-08 1.494473095778248e-09 -6.931989091878815e-11 3.954881675886955e-11 -6.012243121175623e-11 -1.719119683965072e-12 -2.692977629997244e-12 -9.045562571714962e-14 4.882172774892717e-14 -4.738979324521667e-15 7.398810644234422e-15
|
||||
12 -8.432907085842113e-01 1.074564225535518e+00 2.702224533171487e-01 2.104212958222629e-01 1.403908741534795e-02 -1.750301100069031e-02 -8.157176489428349e-04 -7.136652422691409e-04 -3.349027641531190e-05 3.064571625252509e-05 8.979305335863363e-07 1.574060368452125e-06 7.207265063657546e-08 -1.211435670599988e-08 8.501547040936157e-10 -3.005526987365134e-09 -1.049390421906238e-10 -9.274150949045850e-11 -5.617851152512208e-12 2.571369328335004e-12 -4.168828182258284e-15 2.547515238870330e-13 -4.716103679039276e-15 -6.678902592368739e-15
|
||||
12 -2.266727718999265e-01 1.335562335833652e+00 3.362514381326044e-01 4.660635985779042e-02 1.933278197559742e-03 -2.222612138606372e-02 -1.114853098807049e-03 -2.009333075095103e-05 1.016133191717657e-06 5.130704067833834e-05 2.371245554960400e-06 9.891424414335831e-08 2.428697655841655e-08 -1.089731885645080e-07 -4.708017489732315e-09 -2.438412945536230e-09 -1.757718829612977e-10 1.798680842351526e-10 5.496443059256536e-12 1.037427150518911e-11 5.019545981082951e-13 -9.109622310048229e-14 2.404500324827943e-14 6.820041143217459e-16
|
||||
12 4.214765344875847e-01 1.259536998913041e+00 3.020346352781063e-01 -1.190387372877743e-01 -9.821862026320486e-03 -1.796369637757183e-02 -7.400516037404623e-04 6.667823545820309e-04 4.159196549292995e-05 2.616368356013427e-05 1.056473983072004e-06 -2.418744024349654e-06 -1.301506586213971e-07 -5.796549709541788e-08 -3.709228965372416e-09 6.468950846334543e-09 2.967660548028091e-10 2.345716591017921e-10 1.388550418266439e-11 -1.245328208175052e-11 -4.665887065779534e-13 -7.750301215888236e-13 -3.491081175035701e-14 7.216131378687735e-15
|
||||
12 9.271473111817797e-01 9.055877081632260e-01 1.996716148375494e-01 -2.274497569092494e-01 -1.460290373461683e-02 -9.101788058080823e-03 -8.719906495432260e-05 6.927038984227996e-04 2.987648883998367e-05 -1.941671936147276e-05 -1.977657766576566e-06 -1.355747125805320e-06 -6.734568208083129e-08 1.330708638484860e-07 7.661833641689786e-09 3.551411172516433e-09 1.914930192403317e-10 -4.078780532339629e-10 -2.072500795538908e-11 -1.034591296550702e-11 -5.504160584850342e-13 1.012645681382430e-12 6.596662907024004e-14 3.870371509683045e-14
|
||||
12 1.209980802029103e+00 3.998547616681095e-01 8.359259298456899e-02 -2.731750840029819e-01 -1.416216202668445e-02 -2.961155264359851e-03 6.255632437773969e-05 3.444876700395826e-04 -7.997807234747488e-06 -1.451782807389960e-05 -1.055254386949287e-06 1.514914718244730e-06 1.169268186988699e-07 5.367573129488306e-08 2.125121476499890e-09 -7.246598684092562e-09 -4.067234776265382e-10 -6.177283409121161e-11 -5.898853218463184e-13 2.149437296003437e-11 1.108410317364278e-12 -9.608902688154176e-14 -2.011297384221231e-14 -5.614087493301295e-14
|
||||
12 1.264278205173175e+00 -1.582787783096931e-01 -2.949069354036646e-02 -2.818502625684245e-01 -1.438559124910652e-02 8.254100918465356e-04 -8.570203050543733e-05 3.597245119011105e-04 -2.975877169521397e-06 1.371178932745361e-05 1.221789941922816e-06 7.430949077077090e-07 3.780252525664267e-08 -8.613580134670410e-08 -5.245882121128975e-09 -8.599529159842689e-10 3.344177137618122e-11 2.839319310593911e-10 1.380751858727246e-11 -5.637076934843023e-12 -4.469518064341483e-13 -5.970695351423198e-13 -1.219255391527317e-14 3.388526105901839e-14
|
||||
12 1.087673493850061e+00 -6.987759594783819e-01 -1.475442436203200e-01 -2.538283933223078e-01 -1.485492880050208e-02 6.599573974067463e-03 6.813425385408552e-05 5.924507644662786e-04 2.066840899961170e-05 1.006365988193230e-05 7.971681169820085e-07 -8.758096808642510e-07 -4.936887331836301e-08 -3.171174344888671e-08 -4.295547462567284e-10 2.878572263224378e-09 1.467726459763564e-10 -4.742290048825172e-11 -5.257738258974297e-12 -6.105343444880012e-12 -1.831451808224661e-13 3.494136454215428e-13 8.077151789157334e-15 -7.050281830475956e-15
|
||||
|
||||
40
figs/cn.fig/Makefile
Normal file
40
figs/cn.fig/Makefile
Normal file
@ -0,0 +1,40 @@
|
||||
PROJECTNAME=cn cn_short
|
||||
|
||||
PHOTOCOMP_PATH=
|
||||
|
||||
DATS=mc.dat cn.dat mc_short.dat cn_short.dat
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(DATS)
|
||||
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
mc.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=30;E=15e9" mc > $@
|
||||
cn.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;E=15e9;x=0;bmin_cn=-1000;bmax_cn=1000;nx_cn=16000" cn > $@
|
||||
|
||||
mc_short.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=0.0005;J=10;E=15e9" mc > $@
|
||||
cn_short.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=0.0005;E=15e9;x=0;bmin_cn=-1000;bmax_cn=1000;nx_cn=16000" cn > $@
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-dat:
|
||||
rm -f $(DATS)
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
|
||||
clean: clean-aux clean-tex
|
||||
9361
figs/cn.fig/cn.dat
Normal file
9361
figs/cn.fig/cn.dat
Normal file
File diff suppressed because it is too large
Load Diff
25
figs/cn.fig/cn.gnuplot
Normal file
25
figs/cn.fig/cn.gnuplot
Normal file
@ -0,0 +1,25 @@
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,0.5
|
||||
set ytics -0.24,0.12
|
||||
|
||||
set yrange [-0.24:0.24]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot "mc.dat" using 1:5 with lines linestyle 1, \
|
||||
"cn.dat" using 1:3 with lines linestyle 2
|
||||
26
figs/cn.fig/cn_short.dat
Normal file
26
figs/cn.fig/cn_short.dat
Normal file
@ -0,0 +1,26 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=5.845650641658291, E=1.500000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=4.219454049145666e-01 omega=1.550000000000000e-01 m=1.000000000000000e+00, keldysh=1.242825299143273e+00
|
||||
#numerical precision (matching): n_periods=0 NC=12 gl_order=16 J0=1 J=120
|
||||
#numerical precision (Crank-Nicolson): bmin=-1.000000000000000e+03 bmax= 1.000000000000000e+03 nx_cn=16000 mu= 1.000000000000000e-01
|
||||
#
|
||||
# t |psi|^2 current
|
||||
0.000000000000000e+00 1.799999999999999e+00 -2.340555645717801e-16
|
||||
2.631578947368421e-05 1.799930823214389e+00 -1.844039686300892e-03
|
||||
5.263157894736842e-05 1.799724094980058e+00 -3.673701905409824e-03
|
||||
7.894736842105265e-05 1.799382209921303e+00 -5.474798810937662e-03
|
||||
1.052631578947368e-04 1.798909120120437e+00 -7.233518956906041e-03
|
||||
1.315789473684211e-04 1.798310277327859e+00 -8.936608439940258e-03
|
||||
1.578947368421053e-04 1.797592553339864e+00 -1.057154369733800e-02
|
||||
1.842105263157895e-04 1.796764139802528e+00 -1.212669338626712e-02
|
||||
2.105263157894737e-04 1.795834429023747e+00 -1.359146694241804e-02
|
||||
2.368421052631579e-04 1.794813877673240e+00 -1.495644762705038e-02
|
||||
2.631578947368422e-04 1.793713855517177e+00 -1.621350811654198e-02
|
||||
2.894736842105263e-04 1.792546481565754e+00 -1.735590696406148e-02
|
||||
3.157894736842106e-04 1.791324450204648e+00 -1.837836456445107e-02
|
||||
3.421052631578947e-04 1.790060850031863e+00 -1.927711757587828e-02
|
||||
3.684210526315790e-04 1.788768978227520e+00 -2.004995108983447e-02
|
||||
3.947368421052632e-04 1.787462153344070e+00 -2.069620818973520e-02
|
||||
4.210526315789474e-04 1.786153529417339e+00 -2.121677689112625e-02
|
||||
4.473684210526316e-04 1.784855914264545e+00 -2.161405480851675e-02
|
||||
4.736842105263158e-04 1.783581594754897e+00 -2.189189223885764e-02
|
||||
5.000000000000000e-04 1.782342171712728e+00 -2.205551468437851e-02
|
||||
25
figs/cn.fig/cn_short.gnuplot
Normal file
25
figs/cn.fig/cn_short.gnuplot
Normal file
@ -0,0 +1,25 @@
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,0.00025
|
||||
set ytics -0.025,0.005
|
||||
|
||||
set yrange [-0.025:0.005]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot "mc_short.dat" using 1:5 with lines linestyle 1, \
|
||||
"cn_short.dat" using 1:3 with lines linestyle 2
|
||||
606
figs/cn.fig/mc.dat
Normal file
606
figs/cn.fig/mc.dat
Normal file
@ -0,0 +1,606 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=5.845650641658291, E=1.500000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=4.219454049145666e-01 omega=1.550000000000000e-01 m=1.000000000000000e+00, keldysh=1.242825299143273e+00
|
||||
#numerical precision (matching): n_periods=3 NC=12 gl_order=16 J0=1 J=30
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
#% t real(psi0) imag(psi0) abs(psi0)^2 current avgcurrent
|
||||
|
||||
5.000000000000000e-03 9.011237076219065e-01 -9.920990592322099e-01 1.796284479767687e+00 4.066156482056959e-02 0.000000000000000e+00
|
||||
1.000000000000000e-02 9.036959786184608e-01 -9.882977598906416e-01 1.793398883976038e+00 7.201570001853567e-02 0.000000000000000e+00
|
||||
1.500000000000000e-02 9.071741251355965e-01 -9.846371696331014e-01 1.792475249138620e+00 9.663201291162658e-02 0.000000000000000e+00
|
||||
2.000000000000000e-02 9.112296705251185e-01 -9.813857962466512e-01 1.793457593519989e+00 1.156836312659321e-01 0.000000000000000e+00
|
||||
2.500000000000000e-02 9.156315488882216e-01 -9.786363650543179e-01 1.796110268326171e+00 1.300140368375609e-01 0.000000000000000e+00
|
||||
3.000000000000000e-02 9.202092406537398e-01 -9.764097761814351e-01 1.800161097607213e+00 1.403024957858335e-01 0.000000000000000e+00
|
||||
3.500000000000000e-02 9.248342007156113e-01 -9.746926619406401e-01 1.805344084054215e+00 1.471214533034481e-01 0.000000000000000e+00
|
||||
4.000000000000000e-02 9.294087151999519e-01 -9.734546205103959e-01 1.811414458082664e+00 1.509624712076890e-01 0.000000000000000e+00
|
||||
4.500000000000001e-02 9.338584744101831e-01 -9.726571105729394e-01 1.818153504975813e+00 1.522511450122389e-01 0.000000000000000e+00
|
||||
5.000000000000000e-02 9.381272651449116e-01 -9.722583413438044e-01 1.825369047920877e+00 1.513577520549300e-01 0.000000000000000e+00
|
||||
5.500000000000001e-02 9.421730056725623e-01 -9.722160593995715e-01 1.832894038772501e+00 1.486057844547027e-01 0.000000000000000e+00
|
||||
6.000000000000000e-02 9.459647126258931e-01 -9.724891675652013e-01 1.840584418565047e+00 1.442788734682609e-01 0.000000000000000e+00
|
||||
6.500000000000002e-02 9.494801620644853e-01 -9.730386635010360e-01 1.848316818821883e+00 1.386261574576297e-01 0.000000000000000e+00
|
||||
6.999999999999999e-02 9.527040875297279e-01 -9.738281577164219e-01 1.855986359157212e+00 1.318662195761259e-01 0.000000000000000e+00
|
||||
7.500000000000001e-02 9.556267922545760e-01 -9.748241117959209e-01 1.863504615013477e+00 1.241900105915355e-01 0.000000000000000e+00
|
||||
8.000000000000000e-02 9.582430653714695e-01 -9.759958802677270e-01 1.870797730632085e+00 1.157634999719579e-01 0.000000000000000e+00
|
||||
8.499999999999999e-02 9.605512976454061e-01 -9.773156201123415e-01 1.877804616723844e+00 1.067310507759197e-01 0.000000000000000e+00
|
||||
9.000000000000001e-02 9.625527002638457e-01 -9.787581363206964e-01 1.884475190199185e+00 9.722061483045315e-02 0.000000000000000e+00
|
||||
9.500000000000000e-02 9.642505464632329e-01 -9.803007501840784e-01 1.890768677166111e+00 8.735174630418781e-02 0.000000000000000e+00
|
||||
1.000000000000000e-01 9.656494720497791e-01 -9.819232614121206e-01 1.896652194172233e+00 7.717084793097032e-02 0.000000000000000e+00
|
||||
1.050000000000000e-01 9.667560119471850e-01 -9.836073909573243e-01 1.902100686181900e+00 6.692255162050811e-02 0.000000000000000e+00
|
||||
1.100000000000000e-01 9.675773401526806e-01 -9.853368961697180e-01 1.907094708130310e+00 5.649691266971005e-02 0.000000000000000e+00
|
||||
1.150000000000000e-01 9.681214356722894e-01 -9.870972382756389e-01 1.911620072019568e+00 4.606200814956234e-02 0.000000000000000e+00
|
||||
1.200000000000000e-01 9.683968104664674e-01 -9.888754153785958e-01 1.915666969661818e+00 3.564877803455044e-02 0.000000000000000e+00
|
||||
1.250000000000000e-01 9.684123506055112e-01 -9.906597829122454e-01 1.919229286285029e+00 2.530114137575188e-02 0.000000000000000e+00
|
||||
1.300000000000000e-01 9.681771924255469e-01 -9.924398857564037e-01 1.922304002773198e+00 1.507822506166007e-02 0.000000000000000e+00
|
||||
1.350000000000000e-01 9.677006277490590e-01 -9.942063027588171e-01 1.924890677391279e+00 5.028811658825997e-03 0.000000000000000e+00
|
||||
1.400000000000000e-01 9.669920332627706e-01 -9.959505039872319e-01 1.926990998786089e+00 -4.815552690807036e-03 0.000000000000000e+00
|
||||
1.450000000000000e-01 9.660608199938793e-01 -9.976647207498106e-01 1.928608402956044e+00 -1.442979143403208e-02 0.000000000000000e+00
|
||||
1.500000000000000e-01 9.649163995205725e-01 -9.993418282268303e-01 1.929747747707489e+00 -2.378406037313757e-02 0.000000000000000e+00
|
||||
1.550000000000000e-01 9.635681641175022e-01 -1.000975240429556e+00 1.930415038853780e+00 -3.284335335275433e-02 0.000000000000000e+00
|
||||
1.600000000000000e-01 9.620254784938809e-01 -1.002558817128361e+00 1.930617203073199e+00 -4.157586946041263e-02 0.000000000000000e+00
|
||||
1.650000000000000e-01 9.602976811523672e-01 -1.004086782359574e+00 1.930361902935817e+00 -4.995966941801407e-02 0.000000000000000e+00
|
||||
1.700000000000000e-01 9.583940936992136e-01 -1.005553654117106e+00 1.929657390145802e+00 -5.797950092919826e-02 0.000000000000000e+00
|
||||
1.750000000000000e-01 9.563240366834969e-01 -1.006954184848671e+00 1.928512393522870e+00 -6.561621121845297e-02 0.000000000000000e+00
|
||||
1.800000000000000e-01 9.540968507430752e-01 -1.008283312397738e+00 1.926936038657608e+00 -7.284090773107083e-02 0.000000000000000e+00
|
||||
1.850000000000000e-01 9.517219219909825e-01 -1.009536121056629e+00 1.924937796516275e+00 -7.962442670854655e-02 0.000000000000000e+00
|
||||
1.900000000000000e-01 9.492087106924261e-01 -1.010707812426299e+00 1.922527458553933e+00 -8.595458535847925e-02 0.000000000000000e+00
|
||||
1.950000000000000e-01 9.465667823707513e-01 -1.011793685823897e+00 1.919715136160824e+00 -9.182722363193280e-02 0.000000000000000e+00
|
||||
2.000000000000000e-01 9.438058405560354e-01 -1.012789128055572e+00 1.916511282575250e+00 -9.721815185068616e-02 0.000000000000000e+00
|
||||
2.050000000000000e-01 9.409357604783203e-01 -1.013689612295984e+00 1.912926735423699e+00 -1.020526821351758e-01 0.000000000000000e+00
|
||||
2.100000000000000e-01 9.379666228040995e-01 -1.014490705992686e+00 1.908972778040065e+00 -1.063882657623750e-01 0.000000000000000e+00
|
||||
2.150000000000000e-01 9.349087469329699e-01 -1.015188087578326e+00 1.904661218252714e+00 -1.101706611002257e-01 0.000000000000000e+00
|
||||
2.200000000000000e-01 9.317727228903335e-01 -1.015777571954685e+00 1.900004482808620e+00 -1.133900413104608e-01 0.000000000000000e+00
|
||||
2.250000000000000e-01 9.285694412478559e-01 -1.016255144486499e+00 1.895015725914629e+00 -1.160272414311316e-01 0.000000000000000e+00
|
||||
2.300000000000000e-01 9.253101200071022e-01 -1.016617003567798e+00 1.889708950130726e+00 -1.180655564278898e-01 0.000000000000000e+00
|
||||
2.350000000000000e-01 9.220063277661719e-01 -1.016859611493180e+00 1.884099137926923e+00 -1.194931462643198e-01 0.000000000000000e+00
|
||||
2.400000000000000e-01 9.186700022076998e-01 -1.016979753427058e+00 1.878202391836855e+00 -1.202974080986093e-01 0.000000000000000e+00
|
||||
2.450000000000000e-01 9.153134628531312e-01 -1.016974604260638e+00 1.872036080991271e+00 -1.204638831485741e-01 0.000000000000000e+00
|
||||
2.500000000000000e-01 9.119494169894783e-01 -1.016841803064888e+00 1.865618991607702e+00 -1.199813130361806e-01 0.000000000000000e+00
|
||||
2.550000000000000e-01 9.085909576211014e-01 -1.016579534717249e+00 1.858971478676768e+00 -1.188458105767460e-01 0.000000000000000e+00
|
||||
2.600000000000000e-01 9.052515522156862e-01 -1.016186618134238e+00 1.852115615664009e+00 -1.170586389326158e-01 0.000000000000000e+00
|
||||
2.650000000000000e-01 9.019450209187154e-01 -1.015662600396965e+00 1.845075338605188e+00 -1.146201047314932e-01 0.000000000000000e+00
|
||||
2.700000000000000e-01 8.986855028323697e-01 -1.015007855901321e+00 1.837876580542465e+00 -1.115279344508052e-01 0.000000000000000e+00
|
||||
2.750000000000000e-01 8.954874089097231e-01 -1.014223689471419e+00 1.830547391800866e+00 -1.077853458240178e-01 0.000000000000000e+00
|
||||
2.800000000000000e-01 8.923653600008299e-01 -1.013312442116113e+00 1.823118041076731e+00 -1.034120272098875e-01 0.000000000000000e+00
|
||||
2.850000000000000e-01 8.893341085869884e-01 -1.012277597780622e+00 1.815621091664721e+00 -9.844035584892710e-02 0.000000000000000e+00
|
||||
2.900000000000000e-01 8.864084427453910e-01 -1.011123889087757e+00 1.808091446454260e+00 -9.288853999254811e-02 0.000000000000000e+00
|
||||
2.950000000000000e-01 8.836030709374669e-01 -1.009857399765553e+00 1.800566354831367e+00 -8.675599850898540e-02 0.000000000000000e+00
|
||||
3.000000000000000e-01 8.809324864106832e-01 -1.008485661189096e+00 1.793085374437715e+00 -8.007219427298876e-02 0.000000000000000e+00
|
||||
3.050000000000000e-01 8.784108103396230e-01 -1.007017740584994e+00 1.785690281574419e+00 -7.305626273447091e-02 0.000000000000000e+00
|
||||
3.100000000000001e-01 8.760516124362212e-01 -1.005464314978472e+00 1.778424916347230e+00 -6.553493995925624e-02 0.000000000000000e+00
|
||||
3.150000000000001e-01 8.738677093854395e-01 -1.003837730487321e+00 1.771334962656490e+00 -5.769649979124065e-02 0.000000000000000e+00
|
||||
3.200000000000000e-01 8.718709402934262e-01 -1.002152039187683e+00 1.764467646176173e+00 -4.958049646089727e-02 0.000000000000000e+00
|
||||
3.250000000000001e-01 8.700719212878828e-01 -1.000423012108826e+00 1.757871351370484e+00 -4.126084256292895e-02 0.000000000000000e+00
|
||||
3.300000000000000e-01 8.684797788796152e-01 -9.986681190083377e-01 1.751595138246437e+00 -3.284178391143155e-02 0.000000000000000e+00
|
||||
3.350000000000001e-01 8.671018653666038e-01 -9.969064723138004e-01 1.745688159463390e+00 -2.442932739176230e-02 0.000000000000000e+00
|
||||
3.400000000000000e-01 8.659434599578602e-01 -9.951587291959341e-01 1.740198972138656e+00 -1.612544005914524e-02 0.000000000000000e+00
|
||||
3.450000000000000e-01 8.650074598771484e-01 -9.934469451447044e-01 1.735174738460462e+00 -8.037965971194929e-03 0.000000000000000e+00
|
||||
3.500000000000000e-01 8.642940670040686e-01 -9.917943729873040e-01 1.730660312547713e+00 -2.881478804541541e-04 0.000000000000000e+00
|
||||
3.550000000000000e-01 8.638004774254697e-01 -9.902252020303008e-01 1.726697215536420e+00 6.992303030596650e-03 0.000000000000000e+00
|
||||
3.600000000000000e-01 8.635205831789362e-01 -9.887642326147755e-01 1.723322505271976e+00 1.367013521637736e-02 0.000000000000000e+00
|
||||
3.650000000000000e-01 8.634446971691068e-01 -9.874364820132608e-01 1.720567551080175e+00 1.961657877224350e-02 0.000000000000000e+00
|
||||
3.700000000000000e-01 8.635593137061167e-01 -9.862667186439609e-01 1.718456728593305e+00 2.470649305837664e-02 0.000000000000000e+00
|
||||
3.750000000000001e-01 8.638469185805631e-01 -9.852789233319967e-01 1.717006055503393e+00 2.881519802650454e-02 0.000000000000000e+00
|
||||
3.800000000000000e-01 8.642858643259627e-01 -9.844956788543344e-01 1.716221796956533e+00 3.182119826747433e-02 0.000000000000000e+00
|
||||
3.850000000000001e-01 8.648503283430704e-01 -9.839374920356945e-01 1.716099078668609e+00 3.361652151781930e-02 0.000000000000000e+00
|
||||
3.900000000000001e-01 8.655103732973698e-01 -9.836220559053259e-01 1.716620555148773e+00 3.411396730020125e-02 0.000000000000000e+00
|
||||
3.950000000000000e-01 8.662321292375180e-01 -9.835634629016241e-01 1.717755187278399e+00 3.324140413647877e-02 0.000000000000000e+00
|
||||
4.000000000000000e-01 8.669781134065998e-01 -9.837713871688871e-01 1.719457191338263e+00 3.094337198386762e-02 0.000000000000000e+00
|
||||
4.050000000000000e-01 8.677077079037028e-01 -9.842502427932514e-01 1.721665206794072e+00 2.723637326098008e-02 0.000000000000000e+00
|
||||
4.100000000000001e-01 8.683778161436879e-01 -9.849983832157253e-01 1.724301846508074e+00 2.209476698396671e-02 0.000000000000000e+00
|
||||
4.150000000000000e-01 8.689437014886248e-01 -9.860073191203522e-01 1.727273589715656e+00 1.560205756669319e-02 0.000000000000000e+00
|
||||
4.200000000000000e-01 8.693600290104821e-01 -9.872610450554342e-01 1.730471231125055e+00 7.846297660269346e-03 0.000000000000000e+00
|
||||
4.250000000000000e-01 8.695820924478739e-01 -9.887354628261235e-01 1.733770830956011e+00 -1.035540201132523e-03 0.000000000000000e+00
|
||||
4.300000000000000e-01 8.695672443908955e-01 -9.903980178709680e-01 1.737035426320318e+00 -1.084680007508157e-02 0.000000000000000e+00
|
||||
4.350000000000001e-01 8.692765009036419e-01 -9.922075519366803e-01 1.740117461143460e+00 -2.134274130271535e-02 0.000000000000000e+00
|
||||
4.400000000000000e-01 8.686762866570933e-01 -9.941144286138592e-01 1.742861988178616e+00 -3.223970468992605e-02 0.000000000000000e+00
|
||||
4.450000000000000e-01 8.677402817093008e-01 -9.960609964462748e-01 1.745110705142482e+00 -4.321385005812566e-02 0.000000000000000e+00
|
||||
4.500000000000001e-01 8.664513171802860e-01 -9.979824429465377e-01 1.746706841472992e+00 -5.389742409960097e-02 0.000000000000000e+00
|
||||
4.550000000000000e-01 8.648032466541733e-01 -9.998080777675755e-01 1.747500847792893e+00 -6.388365908605911e-02 0.000000000000000e+00
|
||||
4.600000000000000e-01 8.628026997889366e-01 -1.001463070291334e+00 1.747356779920424e+00 -7.274350090150769e-02 0.000000000000000e+00
|
||||
4.650000000000000e-01 8.604706096328609e-01 -1.002870654289274e+00 1.746159219276544e+00 -8.004722275006830e-02 0.000000000000000e+00
|
||||
4.700000000000000e-01 8.578433968051820e-01 -1.003954794924847e+00 1.743820523694843e+00 -8.538066927324336e-02 0.000000000000000e+00
|
||||
4.750000000000000e-01 8.549736893470817e-01 -1.004643286880102e+00 1.740288143349016e+00 -8.835318803302222e-02 0.000000000000000e+00
|
||||
4.800000000000000e-01 8.519304528335815e-01 -1.004871216480972e+00 1.735551658177180e+00 -8.860769239987901e-02 0.000000000000000e+00
|
||||
4.850000000000000e-01 8.487984007541006e-01 -1.004584680032210e+00 1.729649104478137e+00 -8.585023861459024e-02 0.000000000000000e+00
|
||||
4.900000000000000e-01 8.456765583482582e-01 -1.003744612771815e+00 1.722672089008195e+00 -7.990061366109590e-02 0.000000000000000e+00
|
||||
4.950000000000000e-01 8.426758854004104e-01 -1.002330553115008e+00 1.714769185543204e+00 -7.071378914929045e-02 0.000000000000000e+00
|
||||
5.000000000000000e-01 8.399159873617442e-01 -1.000344135371245e+00 1.706147254997497e+00 -5.835125966638677e-02 0.000000000000000e+00
|
||||
5.050000000000000e-01 8.375206698200048e-01 -9.978120607862417e-01 1.697069781026236e+00 -4.287142161971447e-02 0.000000000000000e+00
|
||||
5.100000000000000e-01 8.356128646341928e-01 -9.947882345858943e-01 1.687852491212682e+00 -2.483865965402093e-02 0.000000000000000e+00
|
||||
5.150000000000000e-01 8.343084344071600e-01 -9.913548756039009e-01 1.678855053106552e+00 -4.679849846909717e-03 0.000000000000000e+00
|
||||
5.200000000000000e-01 8.337096489884530e-01 -9.876222087290395e-01 1.670469405991275e+00 1.688665180312902e-02 0.000000000000000e+00
|
||||
5.250000000000000e-01 8.338979709798269e-01 -9.837267198937123e-01 1.663104085437115e+00 3.901746929776945e-02 0.000000000000000e+00
|
||||
5.300000000000000e-01 8.349273314364463e-01 -9.798275269874800e-01 1.657165631421986e+00 6.076120589599165e-02 0.000000000000000e+00
|
||||
5.350000000000000e-01 8.368177592480706e-01 -9.761009073486969e-01 1.653036943519911e+00 8.107430462918896e-02 0.000000000000000e+00
|
||||
5.400000000000000e-01 8.395498916676947e-01 -9.727330564577388e-01 1.651053619724852e+00 9.886663236857389e-02 0.000000000000000e+00
|
||||
5.449999999999999e-01 8.430610282362380e-01 -9.699111880753325e-01 1.651479610084445e+00 1.130652199070324e-01 0.000000000000000e+00
|
||||
5.500000000000000e-01 8.472432932548023e-01 -9.678132219927759e-01 1.654483630629281e+00 1.226816086686652e-01 0.000000000000000e+00
|
||||
5.550000000000000e-01 8.519443287712305e-01 -9.665965120828049e-01 1.660117956496107e+00 1.268776164723573e-01 0.000000000000000e+00
|
||||
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|
||||
2.734999999999999e+00 9.044517114989699e-01 -1.011290195486422e+00 1.840740757920380e+00 -1.213840194802498e-01 4.851110178116397e-05
|
||||
2.739999999999999e+00 8.995655008873580e-01 -1.014659768825537e+00 1.838752536859816e+00 -1.314680731301412e-01 4.737245265424345e-05
|
||||
2.744999999999999e+00 8.941790853913624e-01 -1.016333426907380e+00 1.832489871400633e+00 -1.310846131653416e-01 4.610262327119223e-05
|
||||
2.750000000000000e+00 8.887306075762764e-01 -1.016268334473793e+00 1.822643420497035e+00 -1.205906034133753e-01 4.482584647694386e-05
|
||||
2.754999999999999e+00 8.836435017856302e-01 -1.014533279524117e+00 1.810103613509931e+00 -1.009857670535453e-01 4.354543093231562e-05
|
||||
2.759999999999999e+00 8.792990858764910e-01 -1.011297467923064e+00 1.795889451050833e+00 -7.379194357234774e-02 4.236979929468162e-05
|
||||
2.764999999999999e+00 8.760138871067923e-01 -1.006813027254285e+00 1.781072802252889e+00 -4.090726820891977e-02 4.135146266246344e-05
|
||||
2.769999999999999e+00 8.740231945334469e-01 -1.001393086166345e+00 1.766704657604210e+00 -4.457363054030800e-03 4.060919904177275e-05
|
||||
2.774999999999999e+00 8.734717598466908e-01 -9.953873421250992e-01 1.753748876112544e+00 3.335013566891105e-02 4.007448874696232e-05
|
||||
2.779999999999999e+00 8.744117439481347e-01 -9.891570302143893e-01 1.743027528376968e+00 7.037144249394539e-02 3.981564001882155e-05
|
||||
2.784999999999999e+00 8.768071272171765e-01 -9.830512810604480e-01 1.735180559533426e+00 1.046696928167262e-01 3.986731640561050e-05
|
||||
2.789999999999999e+00 8.805432458590158e-01 -9.773868612197641e-01 1.730641484312954e+00 1.346306150836015e-01 4.025364786960292e-05
|
||||
2.794999999999999e+00 8.854402851183211e-01 -9.724326217944751e-01 1.729629702440490e+00 1.590138834500079e-01 4.090715762482122e-05
|
||||
2.799999999999999e+00 8.912705617116169e-01 -9.683975503209253e-01 1.732157029641310e+00 1.769776880185589e-01 4.177154262996825e-05
|
||||
2.804999999999999e+00 8.977761970431394e-01 -9.654244933025946e-01 1.738046552245813e+00 1.880809796531722e-01 4.290175437340949e-05
|
||||
2.809999999999999e+00 9.046866843255043e-01 -9.635892358805180e-01 1.746962212300675e+00 1.923453929571264e-01 4.414204552674337e-05
|
||||
2.814999999999999e+00 9.117353058767829e-01 -9.629031722515820e-01 1.758443787114390e+00 1.900942508926226e-01 4.546606983218429e-05
|
||||
2.819999999999999e+00 9.186732529828591e-01 -9.633198071063925e-01 1.771945596509605e+00 1.819593986546840e-01 4.685979586584751e-05
|
||||
2.824999999999999e+00 9.252806581680254e-01 -9.647438993930894e-01 1.786875087796039e+00 1.687892982255912e-01 4.824451025711188e-05
|
||||
2.829999999999999e+00 9.313747282768212e-01 -9.670421525574779e-01 1.802629409295723e+00 1.515902229912904e-01 4.953406303129655e-05
|
||||
2.834999999999999e+00 9.368145578249939e-01 -9.700546236331647e-01 1.818627488584919e+00 1.314491718813164e-01 5.063963908704729e-05
|
||||
2.839999999999999e+00 9.415028488498930e-01 -9.736060562972326e-01 1.834336367251114e+00 1.094580441482968e-01 5.162579885022911e-05
|
||||
2.844999999999999e+00 9.453849968818941e-01 -9.775164313820688e-01 1.849291165951314e+00 8.665822173407166e-02 5.241121224059549e-05
|
||||
2.849999999999999e+00 9.484460530362269e-01 -9.816101967938237e-01 1.863108493969606e+00 6.400492692444114e-02 5.296130937970835e-05
|
||||
2.854999999999999e+00 9.507060726599219e-01 -9.857238461418596e-01 1.875493537445152e+00 4.233940916472998e-02 5.324490737000639e-05
|
||||
2.859999999999999e+00 9.522143618804039e-01 -9.897117070556603e-01 1.886241454054334e+00 2.236145662359918e-02 5.331487112157140e-05
|
||||
2.864999999999999e+00 9.530431308634424e-01 -9.934499413705896e-01 1.895233995295221e+00 4.607518723598747e-03 5.311466731431883e-05
|
||||
2.869999999999999e+00 9.532810312067188e-01 -9.968388479031337e-01 1.902432413147392e+00 -1.055263152552190e-02 5.267179058263623e-05
|
||||
2.874999999999999e+00 9.530269767688432e-01 -9.998036190143056e-01 1.907867695043264e+00 -2.289509603282901e-02 5.205290671264736e-05
|
||||
2.879999999999999e+00 9.523845299479708e-01 -1.002293766082129e+00 1.911629086411313e+00 -3.231168631512451e-02 5.124250103770859e-05
|
||||
2.884999999999999e+00 9.514570142045905e-01 -1.004281507309753e+00 1.913851795803465e+00 -3.880131204817039e-02 5.025391556951766e-05
|
||||
2.889999999999999e+00 9.503434354265777e-01 -1.005759467194525e+00 1.914704751109804e+00 -4.249565559655058e-02 4.912884853996137e-05
|
||||
2.894999999999999e+00 9.491352850195701e-01 -1.006737967431805e+00 1.914379124337903e+00 -4.364517654307363e-02 4.788761009466490e-05
|
||||
2.899999999999999e+00 9.479143098149763e-01 -1.007241837526292e+00 1.913077658015344e+00 -4.251889023301739e-02 4.662663063228842e-05
|
||||
2.904999999999999e+00 9.467510178484004e-01 -1.007307283298469e+00 1.911005452783124e+00 -3.914657418445731e-02 4.530208794414321e-05
|
||||
2.909999999999999e+00 9.457039068092340e-01 -1.006978923547819e+00 1.908362431823773e+00 -3.419937430117722e-02 4.395059477945468e-05
|
||||
2.914999999999999e+00 9.448193345337522e-01 -1.006306928960763e+00 1.905337210183244e+00 -2.781175894999525e-02 4.264168406194861e-05
|
||||
2.919999999999999e+00 9.441318663804047e-01 -1.005344510525189e+00 1.902102565958078e+00 -2.035479247088466e-02 4.134693648852850e-05
|
||||
2.924999999999999e+00 9.436650105595440e-01 -1.004145757306089e+00 1.898812354070164e+00 -1.214562192424584e-02 4.011942101974792e-05
|
||||
2.929999999999999e+00 9.434322187068021e-01 -1.002763830816105e+00 1.895599651687028e+00 -3.449015471118240e-03 3.898287685562010e-05
|
||||
2.934999999999999e+00 9.434380607721273e-01 -1.001249532516582e+00 1.892576000878148e+00 5.485895106727420e-03 3.794376249638483e-05
|
||||
2.939999999999999e+00 9.436794919629317e-01 -9.996502244732529e-01 1.889831554840842e+00 1.442253971405652e-02 3.697318438453617e-05
|
||||
2.944999999999999e+00 9.441471410967328e-01 -9.980090689848029e-01 1.887435925817047e+00 2.315425224457108e-02 3.613594196604455e-05
|
||||
2.949999999999999e+00 9.448265645747584e-01 -9.963645486484057e-01 1.885439550929482e+00 3.151559147416701e-02 3.538211138255486e-05
|
||||
2.954999999999999e+00 9.456994257772195e-01 -9.947502269815081e-01 1.883875417995125e+00 3.937811340328699e-02 3.478451610537384e-05
|
||||
2.959999999999999e+00 9.467445733191104e-01 -9.931947089279223e-01 1.882761016951605e+00 4.663885428564447e-02 3.428282467501702e-05
|
||||
2.964999999999999e+00 9.479390019138521e-01 -9.917217605286136e-01 1.882100401655403e+00 5.321412102780114e-02 3.391302714424924e-05
|
||||
2.969999999999999e+00 9.492586868921338e-01 -9.903505487954311e-01 1.881886264139589e+00 5.904238694283432e-02 3.359797860567006e-05
|
||||
2.974999999999999e+00 9.506792892252258e-01 -9.890959669316935e-01 1.882101942762323e+00 6.408840260766342e-02 3.342071335995561e-05
|
||||
2.979999999999999e+00 9.521767337989366e-01 -9.879690158146953e-01 1.882723308597869e+00 6.833843556032662e-02 3.335532641448861e-05
|
||||
2.984999999999999e+00 9.537276700345069e-01 -9.869772183405738e-01 1.883720498112746e+00 7.178899557659296e-02 3.338063211604125e-05
|
||||
2.989999999999999e+00 9.553098287718852e-01 -9.861250470424733e-01 1.885059477352689e+00 7.444714985380274e-02 3.345251436762203e-05
|
||||
2.994999999999999e+00 9.569022877989215e-01 -9.854143472756992e-01 1.886703424211602e+00 7.634448274519776e-02 3.362352834079004e-05
|
||||
206
figs/cn.fig/mc_short.dat
Normal file
206
figs/cn.fig/mc_short.dat
Normal file
@ -0,0 +1,206 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=5.845650641658291, E=1.500000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=4.219454049145666e-01 omega=1.550000000000000e-01 m=1.000000000000000e+00, keldysh=1.242825299143273e+00
|
||||
#numerical precision (matching): n_periods=0 NC=12 gl_order=16 J0=1 J=10
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
#% t real(psi0) imag(psi0) abs(psi0)^2 current avgcurrent
|
||||
|
||||
2.500000000000000e-06 9.000000026987423e-01 -9.949873899004303e-01 1.799999910918607e+00 2.505123638021616e-05 0.000000000000000e+00
|
||||
5.000000000000000e-06 9.000000079987396e-01 -9.949873039976499e-01 1.799999749514243e+00 5.001970807803625e-05 0.000000000000000e+00
|
||||
7.499999999999999e-06 9.000000152074226e-01 -9.949871931480786e-01 1.799999541902053e+00 7.493428466466743e-05 0.000000000000000e+00
|
||||
1.000000000000000e-05 9.000000240763519e-01 -9.949870622582740e-01 1.799999297398785e+00 9.980526327470780e-05 0.000000000000000e+00
|
||||
1.250000000000000e-05 9.000000344612968e-01 -9.949869141639198e-01 1.799999021387775e+00 1.246385943762689e-04 0.000000000000000e+00
|
||||
1.500000000000000e-05 9.000000462645147e-01 -9.949867507782867e-01 1.799998717500461e+00 1.494382922144429e-04 0.000000000000000e+00
|
||||
1.750000000000000e-05 9.000000594139437e-01 -9.949865735059383e-01 1.799998388402190e+00 1.742073027757020e-04 0.000000000000000e+00
|
||||
2.000000000000000e-05 9.000000738535104e-01 -9.949863834351239e-01 1.799998036157632e+00 1.989479076849479e-04 0.000000000000000e+00
|
||||
2.250000000000000e-05 9.000000895379119e-01 -9.949861814413710e-01 1.799997662427530e+00 2.236619419158057e-04 0.000000000000000e+00
|
||||
2.500000000000000e-05 9.000001064295131e-01 -9.949859682489662e-01 1.799997268585467e+00 2.483509230831516e-04 0.000000000000000e+00
|
||||
2.750000000000000e-05 9.000001244963715e-01 -9.949857444700859e-01 1.799996855792175e+00 2.730161337239429e-04 0.000000000000000e+00
|
||||
3.000000000000000e-05 9.000001437109086e-01 -9.949855106310593e-01 1.799996425045406e+00 2.976586764292395e-04 0.000000000000000e+00
|
||||
3.250000000000000e-05 9.000001640489832e-01 -9.949852671907456e-01 1.799995977214836e+00 3.222795123353442e-04 0.000000000000000e+00
|
||||
3.500000000000000e-05 9.000001854892155e-01 -9.949850145538284e-01 1.799995513067304e+00 3.468794888870058e-04 0.000000000000000e+00
|
||||
3.750000000000000e-05 9.000002080124869e-01 -9.949847530807093e-01 1.799995033285600e+00 3.714593604705868e-04 0.000000000000000e+00
|
||||
4.000000000000000e-05 9.000002316015585e-01 -9.949844830950418e-01 1.799994538482766e+00 3.960198041692801e-04 0.000000000000000e+00
|
||||
4.250000000000000e-05 9.000002562407744e-01 -9.949842048895826e-01 1.799994029213215e+00 4.205614321170298e-04 0.000000000000000e+00
|
||||
4.500000000000000e-05 9.000002819158252e-01 -9.949839187308163e-01 1.799993505981496e+00 4.450848014760856e-04 0.000000000000000e+00
|
||||
4.750000000000000e-05 9.000003086135606e-01 -9.949836248626661e-01 1.799992969249355e+00 4.695904227251447e-04 0.000000000000000e+00
|
||||
5.000000000000000e-05 9.000003363218358e-01 -9.949833235095060e-01 1.799992419441440e+00 4.940787676986922e-04 0.000000000000000e+00
|
||||
5.250000000000000e-05 9.000003650293871e-01 -9.949830148786457e-01 1.799991856950030e+00 5.185502619961110e-04 0.000000000000000e+00
|
||||
5.500000000000000e-05 9.000003947257192e-01 -9.949826991623819e-01 1.799991282138909e+00 5.430053161049864e-04 0.000000000000000e+00
|
||||
5.750000000000000e-05 9.000004254010288e-01 -9.949823765397350e-01 1.799990695346692e+00 5.674442987115162e-04 0.000000000000000e+00
|
||||
6.000000000000001e-05 9.000004570461219e-01 -9.949820471779081e-01 1.799990096889569e+00 5.918675607803811e-04 0.000000000000000e+00
|
||||
6.250000000000000e-05 9.000004896523505e-01 -9.949817112335279e-01 1.799989487063671e+00 6.162754302311508e-04 0.000000000000000e+00
|
||||
6.499999999999999e-05 9.000005232115601e-01 -9.949813688537201e-01 1.799988866147105e+00 6.406682136688913e-04 0.000000000000000e+00
|
||||
6.750000000000000e-05 9.000005577160427e-01 -9.949810201770309e-01 1.799988234401713e+00 6.650461995382969e-04 0.000000000000000e+00
|
||||
6.999999999999999e-05 9.000005931584951e-01 -9.949806653342307e-01 1.799987592074591e+00 6.894096605461659e-04 0.000000000000000e+00
|
||||
7.250000000000000e-05 9.000006295319831e-01 -9.949803044490139e-01 1.799986939399418e+00 7.137588551080980e-04 0.000000000000000e+00
|
||||
7.500000000000001e-05 9.000006668299088e-01 -9.949799376386148e-01 1.799986276597622e+00 7.380940282049035e-04 0.000000000000000e+00
|
||||
7.750000000000000e-05 9.000007050459816e-01 -9.949795650143513e-01 1.799985603879412e+00 7.624154121680935e-04 0.000000000000000e+00
|
||||
7.999999999999999e-05 9.000007441741970e-01 -9.949791866821052e-01 1.799984921444692e+00 7.867232276146984e-04 0.000000000000000e+00
|
||||
8.250000000000000e-05 9.000007842088115e-01 -9.949788027427540e-01 1.799984229483880e+00 8.110176844960704e-04 0.000000000000000e+00
|
||||
8.499999999999999e-05 9.000008251443261e-01 -9.949784132925502e-01 1.799983528178629e+00 8.352989831398993e-04 0.000000000000000e+00
|
||||
8.750000000000000e-05 9.000008669754661e-01 -9.949780184234662e-01 1.799982817702478e+00 8.595673151005356e-04 0.000000000000000e+00
|
||||
8.999999999999999e-05 9.000009096971655e-01 -9.949776182235002e-01 1.799982098221435e+00 8.838228638808189e-04 0.000000000000000e+00
|
||||
9.250000000000000e-05 9.000009533045524e-01 -9.949772127769539e-01 1.799981369894500e+00 9.080658055907095e-04 0.000000000000000e+00
|
||||
9.500000000000001e-05 9.000009977929361e-01 -9.949768021646862e-01 1.799980632874145e+00 9.322963094125911e-04 0.000000000000000e+00
|
||||
9.750000000000000e-05 9.000010431577971e-01 -9.949763864643406e-01 1.799979887306760e+00 9.565145368258448e-04 0.000000000000000e+00
|
||||
1.000000000000000e-04 9.000010893947743e-01 -9.949759657505540e-01 1.799979133333028e+00 9.807206436436005e-04 0.000000000000000e+00
|
||||
1.025000000000000e-04 9.000011364996567e-01 -9.949755400951461e-01 1.799978371088301e+00 1.004914770236470e-03 0.000000000000000e+00
|
||||
1.050000000000000e-04 9.000011844683721e-01 -9.949751095672856e-01 1.799977600702904e+00 1.029097074952171e-03 0.000000000000000e+00
|
||||
1.075000000000000e-04 9.000012332969818e-01 -9.949746742336602e-01 1.799976822302466e+00 1.053267685734603e-03 0.000000000000000e+00
|
||||
1.100000000000000e-04 9.000012829816718e-01 -9.949742341586116e-01 1.799976036008171e+00 1.077426741057826e-03 0.000000000000000e+00
|
||||
1.125000000000000e-04 9.000013335187437e-01 -9.949737894042753e-01 1.799975241937020e+00 1.101574371320983e-03 0.000000000000000e+00
|
||||
1.150000000000000e-04 9.000013849046112e-01 -9.949733400307014e-01 1.799974440202067e+00 1.125710699724602e-03 0.000000000000000e+00
|
||||
1.175000000000000e-04 9.000014371357941e-01 -9.949728860959717e-01 1.799973630912642e+00 1.149835845844864e-03 0.000000000000000e+00
|
||||
1.200000000000000e-04 9.000014902089115e-01 -9.949724276563023e-01 1.799972814174537e+00 1.173949926856538e-03 0.000000000000000e+00
|
||||
1.225000000000000e-04 9.000015441206771e-01 -9.949719647661428e-01 1.799971990090202e+00 1.198053056774876e-03 0.000000000000000e+00
|
||||
1.250000000000000e-04 9.000015988678952e-01 -9.949714974782647e-01 1.799971158758908e+00 1.222145345472817e-03 0.000000000000000e+00
|
||||
1.275000000000000e-04 9.000016544474538e-01 -9.949710258438474e-01 1.799970320276913e+00 1.246226898670683e-03 0.000000000000000e+00
|
||||
1.300000000000000e-04 9.000017108563232e-01 -9.949705499125563e-01 1.799969474737604e+00 1.270297818864217e-03 0.000000000000000e+00
|
||||
1.325000000000000e-04 9.000017680915511e-01 -9.949700697326161e-01 1.799968622231646e+00 1.294358206272734e-03 0.000000000000000e+00
|
||||
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|
||||
4.225000000000001e-04 9.000135287783656e-01 -9.948929187763793e-01 1.799836271815469e+00 4.029150335014739e-03 0.000000000000000e+00
|
||||
4.250000000000001e-04 9.000136714885074e-01 -9.948921081460035e-01 1.799834915717422e+00 4.052322553410062e-03 0.000000000000000e+00
|
||||
4.275000000000001e-04 9.000138148699502e-01 -9.948912954741305e-01 1.799833556766954e+00 4.075488786660303e-03 0.000000000000000e+00
|
||||
4.300000000000001e-04 9.000139589220032e-01 -9.948904807687426e-01 1.799832194978717e+00 4.098649049582350e-03 0.000000000000000e+00
|
||||
4.325000000000001e-04 9.000141036439802e-01 -9.948896640377544e-01 1.799830830367233e+00 4.121803358270565e-03 0.000000000000000e+00
|
||||
4.350000000000001e-04 9.000142490352002e-01 -9.948888452890112e-01 1.799829462946898e+00 4.144951730214750e-03 0.000000000000000e+00
|
||||
4.375000000000001e-04 9.000143950949870e-01 -9.948880245302907e-01 1.799828092731980e+00 4.168094182464684e-03 0.000000000000000e+00
|
||||
4.400000000000001e-04 9.000145418226686e-01 -9.948872017693028e-01 1.799826719736621e+00 4.191230729612325e-03 0.000000000000000e+00
|
||||
4.425000000000001e-04 9.000146892175750e-01 -9.948863770136920e-01 1.799825343974838e+00 4.214361384772277e-03 0.000000000000000e+00
|
||||
4.450000000000001e-04 9.000148372790407e-01 -9.948855502710348e-01 1.799823965460518e+00 4.237486164511694e-03 0.000000000000000e+00
|
||||
4.475000000000000e-04 9.000149860064053e-01 -9.948847215488478e-01 1.799822584207438e+00 4.260605089648413e-03 0.000000000000000e+00
|
||||
4.500000000000001e-04 9.000151353990121e-01 -9.948838908545823e-01 1.799821200229254e+00 4.283718178531454e-03 0.000000000000000e+00
|
||||
4.525000000000001e-04 9.000152854562117e-01 -9.948830581956293e-01 1.799819813539514e+00 4.306825412658727e-03 0.000000000000000e+00
|
||||
4.550000000000001e-04 9.000154361773501e-01 -9.948822235793129e-01 1.799818424151624e+00 4.329926850340258e-03 0.000000000000000e+00
|
||||
4.575000000000001e-04 9.000155875617865e-01 -9.948813870129042e-01 1.799817032078908e+00 4.353022482414880e-03 0.000000000000000e+00
|
||||
4.600000000000001e-04 9.000157396088784e-01 -9.948805485036086e-01 1.799815637334557e+00 4.376112331468954e-03 0.000000000000000e+00
|
||||
4.625000000000001e-04 9.000158923179877e-01 -9.948797080585733e-01 1.799814239931656e+00 4.399196413168756e-03 0.000000000000000e+00
|
||||
4.650000000000001e-04 9.000160456884810e-01 -9.948788656848886e-01 1.799812839883181e+00 4.422274738270543e-03 0.000000000000000e+00
|
||||
4.675000000000001e-04 9.000161997197278e-01 -9.948780213895863e-01 1.799811437201999e+00 4.445347319356439e-03 0.000000000000000e+00
|
||||
4.700000000000001e-04 9.000163544111031e-01 -9.948771751796437e-01 1.799810031900880e+00 4.468414172165045e-03 0.000000000000000e+00
|
||||
4.725000000000001e-04 9.000165097619830e-01 -9.948763270619811e-01 1.799808623992480e+00 4.491475312916175e-03 0.000000000000000e+00
|
||||
4.750000000000001e-04 9.000166657717489e-01 -9.948754770434639e-01 1.799807213489356e+00 4.514530755782831e-03 0.000000000000000e+00
|
||||
4.775000000000002e-04 9.000168224397844e-01 -9.948746251309010e-01 1.799805800403957e+00 4.537580512872471e-03 0.000000000000000e+00
|
||||
4.800000000000001e-04 9.000169797654768e-01 -9.948737713310487e-01 1.799804384748634e+00 4.560624596345456e-03 0.000000000000000e+00
|
||||
4.825000000000001e-04 9.000171377482170e-01 -9.948729156506110e-01 1.799802966535641e+00 4.583663020319781e-03 0.000000000000000e+00
|
||||
4.850000000000001e-04 9.000172963873996e-01 -9.948720580962381e-01 1.799801545777129e+00 4.606695800482083e-03 0.000000000000000e+00
|
||||
4.875000000000001e-04 9.000174556824224e-01 -9.948711986745310e-01 1.799800122485159e+00 4.629722951322276e-03 0.000000000000000e+00
|
||||
4.900000000000001e-04 9.000176156326871e-01 -9.948703373920385e-01 1.799798696671696e+00 4.652744483891761e-03 0.000000000000000e+00
|
||||
4.925000000000001e-04 9.000177762375979e-01 -9.948694742552578e-01 1.799797268348604e+00 4.675760408109110e-03 0.000000000000000e+00
|
||||
4.950000000000001e-04 9.000179374965607e-01 -9.948686092706376e-01 1.799795837527656e+00 4.698770740000343e-03 0.000000000000000e+00
|
||||
4.975000000000001e-04 9.000180994089861e-01 -9.948677424445761e-01 1.799794404220531e+00 4.721775500910389e-03 0.000000000000000e+00
|
||||
38
figs/current.fig/Makefile
Normal file
38
figs/current.fig/Makefile
Normal file
@ -0,0 +1,38 @@
|
||||
PROJECTNAME=current01 current05 current18 current30
|
||||
|
||||
PHOTOCOMP_PATH=
|
||||
|
||||
DATS=mc01.dat mc05.dat mc18.dat mc30.dat
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(DATS)
|
||||
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
mc01.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=30;E=1e9" mc > $@
|
||||
mc05.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=30;E=5e9" mc > $@
|
||||
mc18.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=60;E=1.8642379487149097e10" mc > $@
|
||||
mc30.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=60;E=30e9" mc > $@
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-dat:
|
||||
rm -f $(DATS)
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
|
||||
clean: clean-aux clean-tex
|
||||
29
figs/current.fig/current01.gnuplot
Normal file
29
figs/current.fig/current01.gnuplot
Normal file
@ -0,0 +1,29 @@
|
||||
set title "$E=1\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
#
|
||||
## start ticks at 0, then every x
|
||||
set xtics 0,1
|
||||
set ytics -0.008,0.004
|
||||
|
||||
set yrange [-0.011:0.011]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#000000" linewidth 1
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot 0 with lines linestyle 3 ,\
|
||||
cos(2*pi*x) axes x1y2 linetype 0 linewidth 2,\
|
||||
"mc01.dat" using 1:5 with lines linestyle 1
|
||||
29
figs/current.fig/current05.gnuplot
Normal file
29
figs/current.fig/current05.gnuplot
Normal file
@ -0,0 +1,29 @@
|
||||
set title "$E=5\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
#
|
||||
## start ticks at 0, then every x
|
||||
set xtics 0,1
|
||||
set ytics -0.04,0.02
|
||||
|
||||
set yrange [-0.05:0.05]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#000000" linewidth 1
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot 0 with lines linestyle 3 ,\
|
||||
cos(2*pi*x) axes x1y2 linetype 0 linewidth 2,\
|
||||
"mc05.dat" using 1:5 with lines linestyle 1
|
||||
29
figs/current.fig/current18.gnuplot
Normal file
29
figs/current.fig/current18.gnuplot
Normal file
@ -0,0 +1,29 @@
|
||||
set title "$E=18.6\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
#
|
||||
## start ticks at 0, then every x
|
||||
set xtics 0,1
|
||||
set ytics -0.4,0.2
|
||||
|
||||
set yrange [-0.4:0.4]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#000000" linewidth 1
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot 0 with lines linestyle 3 ,\
|
||||
cos(2*pi*x) axes x1y2 linetype 0 linewidth 2,\
|
||||
"mc18.dat" using 1:5 with lines linestyle 1
|
||||
29
figs/current.fig/current30.gnuplot
Normal file
29
figs/current.fig/current30.gnuplot
Normal file
@ -0,0 +1,29 @@
|
||||
set title "$E=30\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
#
|
||||
## start ticks at 0, then every x
|
||||
set xtics 0,1
|
||||
set ytics -0.8,0.4
|
||||
|
||||
set yrange [-0.85:0.85]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#000000" linewidth 1
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot 0 with lines linestyle 3 ,\
|
||||
cos(2*pi*x) axes x1y2 linetype 0 linewidth 2,\
|
||||
"mc30.dat" using 1:5 with lines linestyle 1
|
||||
606
figs/current.fig/mc01.dat
Normal file
606
figs/current.fig/mc01.dat
Normal file
@ -0,0 +1,606 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=3.558597156973679, E=1.000000000000000e+09 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=2.812969366097111e-02 omega=1.550000000000000e-01 m=1.000000000000000e+00
|
||||
#numerical precision (matching): n_periods=3 NC=12 gl_order=16 J0=1 J=30
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
# t real(psi0) imag(psi0) abs(psi0)^2 current avgcurrent
|
||||
|
||||
5.000000000000000e-03 9.869413613109341e-01 -9.086799130898394e-01 1.799752435119238e+00 2.719081453552717e-03 0.000000000000000e+00
|
||||
1.000000000000000e-02 1.065729134991043e+00 -8.147301241354055e-01 1.799563764342449e+00 4.829458439071494e-03 0.000000000000000e+00
|
||||
1.500000000000000e-02 1.135671839528658e+00 -7.139774489506698e-01 1.799514324708513e+00 6.487704215104906e-03 0.000000000000000e+00
|
||||
2.000000000000000e-02 1.196170732561787e+00 -6.072725084716197e-01 1.799604320982816e+00 7.757685662635345e-03 0.000000000000000e+00
|
||||
2.500000000000000e-02 1.246713028265988e+00 -4.955073230882093e-01 1.799820882082194e+00 8.684568998241380e-03 0.000000000000000e+00
|
||||
3.000000000000000e-02 1.286872439201503e+00 -3.796133440895249e-01 1.800146965787257e+00 9.306691531577477e-03 0.000000000000000e+00
|
||||
3.500000000000000e-02 1.316311244028597e+00 -2.605554339156567e-01 1.800564425299088e+00 9.658439836002593e-03 0.000000000000000e+00
|
||||
4.000000000000000e-02 1.334782426288183e+00 -1.393244477957598e-01 1.801055427281363e+00 9.771007195382630e-03 0.000000000000000e+00
|
||||
4.500000000000001e-02 1.342131326032755e+00 -1.692917733358443e-02 1.801603093363633e+00 9.673018556568182e-03 0.000000000000000e+00
|
||||
5.000000000000000e-02 1.338296618593865e+00 1.056119898537878e-01 1.802191731740648e+00 9.391304345413876e-03 0.000000000000000e+00
|
||||
5.500000000000001e-02 1.323310586260089e+00 2.272795102334836e-01 1.802806883479991e+00 8.951557929817441e-03 0.000000000000000e+00
|
||||
6.000000000000000e-02 1.297298689124593e+00 3.470611334365802e-01 1.803435319146671e+00 8.378585449086925e-03 0.000000000000000e+00
|
||||
6.500000000000002e-02 1.260478431863600e+00 4.639603108620658e-01 1.804065047248544e+00 7.696048692720002e-03 0.000000000000000e+00
|
||||
6.999999999999999e-02 1.213157503941054e+00 5.770045148077980e-01 1.804685339477070e+00 6.925849161108032e-03 0.000000000000000e+00
|
||||
7.500000000000001e-02 1.155731166482918e+00 6.852533952508416e-01 1.805286744882772e+00 6.087512002098357e-03 0.000000000000000e+00
|
||||
8.000000000000000e-02 1.088678880036877e+00 7.878066738866744e-01 1.805861059258733e+00 5.198049911455303e-03 0.000000000000000e+00
|
||||
8.499999999999999e-02 1.012560210411564e+00 8.838116638750808e-01 1.806401236910350e+00 4.272792910606049e-03 0.000000000000000e+00
|
||||
9.000000000000001e-02 9.280101008045862e-01 9.724703230417560e-01 1.806901276392276e+00 3.327552334725608e-03 0.000000000000000e+00
|
||||
9.500000000000000e-02 8.357336370077447e-01 1.053045802364078e+00 1.807356173902796e+00 2.382252874213052e-03 0.000000000000000e+00
|
||||
1.000000000000000e-01 7.365003690712160e-01 1.124868559350770e+00 1.807762069457916e+00 1.406711698966647e-03 0.000000000000000e+00
|
||||
1.050000000000000e-01 6.311372090085361e-01 1.187342282256846e+00 1.808115871829981e+00 5.386028218271248e-04 0.000000000000000e+00
|
||||
1.100000000000000e-01 5.205221441416628e-01 1.239948438243014e+00 1.808415432043124e+00 -3.583544316679970e-04 0.000000000000000e+00
|
||||
1.150000000000000e-01 4.055766267423430e-01 1.282250751100720e+00 1.808659388858058e+00 -1.198388516981143e-03 0.000000000000000e+00
|
||||
1.200000000000000e-01 2.872579278497024e-01 1.313898780406375e+00 1.808847122265865e+00 -1.994465245766268e-03 0.000000000000000e+00
|
||||
1.250000000000000e-01 1.665511505623108e-01 1.334630812516835e+00 1.808978691472976e+00 -2.744807188548084e-03 0.000000000000000e+00
|
||||
1.300000000000000e-01 4.446101649706951e-02 1.344276010082564e+00 1.809054773271451e+00 -3.435823673779609e-03 0.000000000000000e+00
|
||||
1.350000000000000e-01 -7.799650599607943e-02 1.342755802834180e+00 1.809076600992460e+00 -4.059691243795858e-03 0.000000000000000e+00
|
||||
1.400000000000000e-01 -1.998026620404535e-01 1.330084508808644e+00 1.809045904331184e+00 -4.617227846331193e-03 0.000000000000000e+00
|
||||
1.450000000000000e-01 -3.199443883964239e-01 1.306369181606065e+00 1.808964850316461e+00 -5.110870810908170e-03 0.000000000000000e+00
|
||||
1.500000000000000e-01 -4.374227390521901e-01 1.271808685700511e+00 1.808835985663182e+00 -5.539334941442912e-03 0.000000000000000e+00
|
||||
1.550000000000000e-01 -5.512611882256536e-01 1.226692008239744e+00 1.808662180723215e+00 -5.898886286822612e-03 0.000000000000000e+00
|
||||
1.600000000000000e-01 -6.605137418661915e-01 1.171395822106470e+00 1.808446575242570e+00 -6.188071960293706e-03 0.000000000000000e+00
|
||||
1.650000000000000e-01 -7.642727904317264e-01 1.106381321214255e+00 1.808192526126098e+00 -6.410009525011614e-03 0.000000000000000e+00
|
||||
1.700000000000000e-01 -8.616766379609136e-01 1.032190355016052e+00 1.807903557395787e+00 -6.569785517020628e-03 0.000000000000000e+00
|
||||
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|
||||
2.894999999999999e+00 -1.860832131417970e-01 1.330398849319796e+00 1.804588060484613e+00 2.482510469259203e-03 3.765382479655473e-07
|
||||
2.899999999999999e+00 -3.065490296875732e-01 1.307983195323427e+00 1.804792346850875e+00 2.362885880411928e-03 3.967275580745592e-07
|
||||
2.904999999999999e+00 -4.244751187451442e-01 1.274681254554809e+00 1.804991427147125e+00 2.309687915316504e-03 3.858277730558440e-07
|
||||
2.909999999999999e+00 -5.388796776917639e-01 1.230769572495605e+00 1.805185047610193e+00 2.206461746242728e-03 3.775084600781653e-07
|
||||
2.914999999999999e+00 -6.488101909201281e-01 1.176613065166379e+00 1.805372968962035e+00 2.114444165178784e-03 3.759382881788785e-07
|
||||
2.919999999999999e+00 -7.533513683619829e-01 1.112661980484754e+00 1.805554967029127e+00 2.018486123488227e-03 3.527169948391569e-07
|
||||
2.924999999999999e+00 -8.516327736388993e-01 1.039448147859652e+00 1.805730833224745e+00 1.917031214676986e-03 3.233186126631240e-07
|
||||
2.929999999999999e+00 -9.428360781437184e-01 9.575805473231049e-01 1.805900374861045e+00 1.815469869463351e-03 2.981809929044611e-07
|
||||
2.934999999999999e+00 -1.026201880478106e+00 8.677402352184547e-01 1.806063415313781e+00 1.715114301132130e-03 2.892257825557708e-07
|
||||
2.939999999999999e+00 -1.101036034316621e+00 7.706746688332167e-01 1.806219794044859e+00 1.614016514810150e-03 2.493766023356400e-07
|
||||
2.944999999999999e+00 -1.166715431879427e+00 6.671914773864709e-01 1.806369366482739e+00 1.511367655418952e-03 2.155069171109803e-07
|
||||
2.949999999999999e+00 -1.222693194750410e+00 5.581517314096173e-01 1.806512003764516e+00 1.408317284856904e-03 1.713621201977018e-07
|
||||
2.954999999999999e+00 -1.268503228738856e+00 4.444627667519575e-01 1.806647592349708e+00 1.305639367813064e-03 1.442297209848677e-07
|
||||
2.959999999999999e+00 -1.303764104807643e+00 3.270706231604217e-01 1.806776033519422e+00 1.202437247275521e-03 1.007322444250693e-07
|
||||
2.964999999999999e+00 -1.328182233730964e+00 2.069521605968866e-01 1.806897242774294e+00 1.097907628770412e-03 7.027657922326793e-08
|
||||
2.969999999999999e+00 -1.341554308053387e+00 8.510691914035259e-02 1.807011149142165e+00 9.935965691211411e-04 2.426415949044503e-08
|
||||
2.974999999999999e+00 -1.343768991050522e+00 -3.745120954411874e-02 1.807117694405256e+00 8.919605713811325e-04 -2.012810447868533e-08
|
||||
2.979999999999999e+00 -1.334807838691192e+00 -1.597024296237216e-01 1.807216832259172e+00 7.914943198702116e-04 -5.816686688494834e-08
|
||||
2.984999999999999e+00 -1.314745447017525e+00 -2.806295368773336e-01 1.807308527421299e+00 6.864171305228456e-04 -9.128041575280858e-08
|
||||
2.989999999999999e+00 -1.283748823836313e+00 -3.992263919235427e-01 1.807392754709406e+00 5.790142691096547e-04 -1.326606628872558e-07
|
||||
2.994999999999999e+00 -1.242075990094079e+00 -5.145063001907394e-01 1.807469498104150e+00 4.860145777730379e-04 -1.592566057954533e-07
|
||||
606
figs/current.fig/mc05.dat
Normal file
606
figs/current.fig/mc05.dat
Normal file
@ -0,0 +1,606 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=3.803638601761316, E=5.000000000000000e+09 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=1.406484683048555e-01 omega=1.550000000000000e-01 m=1.000000000000000e+00
|
||||
#numerical precision (matching): n_periods=3 NC=12 gl_order=16 J0=1 J=30
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
#% t real(psi0) imag(psi0) abs(psi0)^2 current avgcurrent
|
||||
|
||||
5.000000000000000e-03 9.871712211657485e-01 -9.078849796854442e-01 1.798762156236315e+00 1.358367476325980e-02 0.000000000000000e+00
|
||||
1.000000000000000e-02 1.066385854453090e+00 -8.127942114708884e-01 1.797813220778229e+00 2.410687891270248e-02 0.000000000000000e+00
|
||||
1.500000000000000e-02 1.136800629588420e+00 -7.107971297127322e-01 1.797548231040486e+00 3.237430698120528e-02 0.000000000000000e+00
|
||||
2.000000000000000e-02 1.197742605511726e+00 -6.028062645260565e-01 1.797962741609878e+00 3.872718338390371e-02 0.000000000000000e+00
|
||||
2.500000000000000e-02 1.248654650638362e+00 -4.897439218905649e-01 1.798987545589560e+00 4.340909766588012e-02 0.000000000000000e+00
|
||||
3.000000000000000e-02 1.289082383494650e+00 -3.725617281252825e-01 1.800535632699945e+00 4.662213459012694e-02 0.000000000000000e+00
|
||||
3.500000000000000e-02 1.318670406080714e+00 -2.522410384524204e-01 1.802517181352630e+00 4.854358814374831e-02 0.000000000000000e+00
|
||||
4.000000000000000e-02 1.337161479422427e+00 -1.297877698481467e-01 1.804845687253330e+00 4.933223613054408e-02 0.000000000000000e+00
|
||||
4.500000000000001e-02 1.344396442581795e+00 -6.225082981947669e-03 1.807440546484719e+00 4.913190260108297e-02 0.000000000000000e+00
|
||||
5.000000000000000e-02 1.340314044512688e+00 1.174148180933628e-01 1.810227977425857e+00 4.807425693804794e-02 0.000000000000000e+00
|
||||
5.500000000000001e-02 1.324950388790951e+00 2.400992179022112e-01 1.813141167194546e+00 4.628097116969072e-02 0.000000000000000e+00
|
||||
6.000000000000000e-02 1.298437880260942e+00 3.608035172088717e-01 1.816120106926820e+00 4.386497168525309e-02 0.000000000000000e+00
|
||||
6.500000000000002e-02 1.261003603240967e+00 4.785198584560150e-01 1.819111342323465e+00 4.093070330547007e-02 0.000000000000000e+00
|
||||
6.999999999999999e-02 1.212967053488843e+00 5.922656855822559e-01 1.822067715167624e+00 3.757368266331554e-02 0.000000000000000e+00
|
||||
7.500000000000001e-02 1.154737147224175e+00 7.010921509244420e-01 1.824948083267287e+00 3.387995348045743e-02 0.000000000000000e+00
|
||||
8.000000000000000e-02 1.086808466047370e+00 8.040922406749329e-01 1.827716973385871e+00 2.992625865155845e-02 0.000000000000000e+00
|
||||
8.499999999999999e-02 1.009756767291415e+00 9.004084687564468e-01 1.830344139699138e+00 2.578175555752242e-02 0.000000000000000e+00
|
||||
9.000000000000001e-02 9.242338760487722e-01 9.892400139427835e-01 1.832804062821656e+00 2.151190014947962e-02 0.000000000000000e+00
|
||||
9.500000000000000e-02 8.309621459436678e-01 1.069849257653506e+00 1.835075522093063e+00 1.718471833849624e-02 0.000000000000000e+00
|
||||
1.000000000000000e-01 7.307285879015526e-01 1.141567868548147e+00 1.837141467678157e+00 1.278441061766251e-02 0.000000000000000e+00
|
||||
1.050000000000000e-01 6.243770801654467e-01 1.203803071899028e+00 1.838988574149464e+00 8.559699227324300e-03 0.000000000000000e+00
|
||||
1.100000000000000e-01 5.128021057140687e-01 1.256041751222323e+00 1.840606880438423e+00 4.318244769790593e-03 0.000000000000000e+00
|
||||
1.150000000000000e-01 3.969407082053431e-01 1.297854994955250e+00 1.841989513760853e+00 2.202536806175301e-04 0.000000000000000e+00
|
||||
1.200000000000000e-01 2.777646056639680e-01 1.328901507334238e+00 1.843132392354869e+00 -3.735288854365113e-03 0.000000000000000e+00
|
||||
1.250000000000000e-01 1.562719664303641e-01 1.348930325795811e+00 1.844033951343605e+00 -7.528305281783580e-03 0.000000000000000e+00
|
||||
1.300000000000000e-01 3.347898932680503e-02 1.357782767154020e+00 1.844694885506772e+00 -1.112157760994082e-02 0.000000000000000e+00
|
||||
1.350000000000000e-01 -8.958864050230819e-02 1.355393589992290e+00 1.845117908299240e+00 -1.448916507913665e-02 0.000000000000000e+00
|
||||
1.400000000000000e-01 -2.119043479258534e-01 1.341791367497533e+00 1.845307526560782e+00 -1.762123554926971e-02 0.000000000000000e+00
|
||||
1.450000000000000e-01 -3.324492441900166e-01 1.317098071659346e+00 1.845269830331281e+00 -2.051248224858198e-02 0.000000000000000e+00
|
||||
1.500000000000000e-01 -4.502206117939621e-01 1.281527876341805e+00 1.845012297125266e+00 -2.315299425809048e-02 0.000000000000000e+00
|
||||
1.550000000000000e-01 -5.642402275924931e-01 1.235385193187038e+00 1.844543609979403e+00 -2.553004289945627e-02 0.000000000000000e+00
|
||||
1.600000000000000e-01 -6.735624556644608e-01 1.179061960583770e+00 1.843873488576381e+00 -2.763588228080878e-02 0.000000000000000e+00
|
||||
1.650000000000000e-01 -7.772820438788156e-01 1.113034211971503e+00 1.843012532755454e+00 -2.947174310464764e-02 0.000000000000000e+00
|
||||
1.700000000000000e-01 -8.745415610149438e-01 1.037857955494717e+00 1.841972077726128e+00 -3.104355736988386e-02 0.000000000000000e+00
|
||||
1.750000000000000e-01 -9.645384147021856e-01 9.541644024290460e-01 1.840764060298984e+00 -3.235453100920871e-02 0.000000000000000e+00
|
||||
1.800000000000000e-01 -1.046531394290580e+00 8.626545868456317e-01 1.839400895441593e+00 -3.340410581846142e-02 0.000000000000000e+00
|
||||
1.850000000000000e-01 -1.119846687018268e+00 7.640934236380938e-01 1.837895362472775e+00 -3.419586876356898e-02 0.000000000000000e+00
|
||||
1.900000000000000e-01 -1.183883320475284e+00 6.593032562752210e-01 1.836260500234693e+00 -3.474245579096692e-02 0.000000000000000e+00
|
||||
1.950000000000000e-01 -1.238117989341009e+00 5.491569494084579e-01 1.834509510613426e+00 -3.505359008803550e-02 0.000000000000000e+00
|
||||
2.000000000000000e-01 -1.282109229617432e+00 4.345705846971133e-01 1.832655669754196e+00 -3.512972017978674e-02 0.000000000000000e+00
|
||||
2.050000000000000e-01 -1.315500908989887e+00 3.164958211306004e-01 1.830712246346353e+00 -3.500681791497350e-02 0.000000000000000e+00
|
||||
2.100000000000000e-01 -1.338025007701029e+00 1.959119833610219e-01 1.828692426457790e+00 -3.466668969240159e-02 0.000000000000000e+00
|
||||
2.150000000000000e-01 -1.349503670061092e+00 7.381794334179170e-02 1.826609244267569e+00 -3.414461747461597e-02 0.000000000000000e+00
|
||||
2.200000000000000e-01 -1.349850512679344e+00 -4.877613812695805e-02 1.824475518231266e+00 -3.344640483463485e-02 0.000000000000000e+00
|
||||
2.250000000000000e-01 -1.339071181440215e+00 -1.708571425883267e-01 1.822303792137139e+00 -3.258040829175987e-02 0.000000000000000e+00
|
||||
2.300000000000000e-01 -1.317263155264659e+00 -2.914173303178731e-01 1.820106280627402e+00 -3.156756118344205e-02 0.000000000000000e+00
|
||||
2.350000000000000e-01 -1.284614800615814e+00 -4.094626145975695e-01 1.817894818714285e+00 -3.042955961331207e-02 0.000000000000000e+00
|
||||
2.400000000000000e-01 -1.241403686622434e+00 -5.240207073673282e-01 1.815680814909526e+00 -2.917991994303480e-02 0.000000000000000e+00
|
||||
2.450000000000000e-01 -1.187994176467644e+00 -6.341490710426072e-01 1.813475207625239e+00 -2.782773130019936e-02 0.000000000000000e+00
|
||||
2.500000000000000e-01 -1.124834316311133e+00 -7.389426130527204e-01 1.811288424536318e+00 -2.638683540755939e-02 0.000000000000000e+00
|
||||
2.550000000000000e-01 -1.052452048453376e+00 -8.375410618844775e-01 1.809130344636286e+00 -2.487896115563272e-02 0.000000000000000e+00
|
||||
2.600000000000000e-01 -9.714507806723772e-01 -9.291359661001745e-01 1.807010262769875e+00 -2.332717753263415e-02 0.000000000000000e+00
|
||||
2.650000000000000e-01 -8.825043486254809e-01 -1.012977260917834e+00 1.804936856479481e+00 -2.174678634518071e-02 0.000000000000000e+00
|
||||
2.700000000000000e-01 -7.863514128745072e-01 -1.088379350467209e+00 1.802918155053157e+00 -2.014461814228740e-02 0.000000000000000e+00
|
||||
2.750000000000000e-01 -6.837893364336505e-01 -1.154726657736984e+00 1.800961510708799e+00 -1.853011826580408e-02 0.000000000000000e+00
|
||||
2.800000000000000e-01 -5.756675927323662e-01 -1.211478598480434e+00 1.799073571898395e+00 -1.692689551176024e-02 0.000000000000000e+00
|
||||
2.850000000000000e-01 -4.628807575042316e-01 -1.258173939924970e+00 1.797260258774013e+00 -1.536474482001961e-02 0.000000000000000e+00
|
||||
2.900000000000000e-01 -3.463611413250711e-01 -1.294434510009090e+00 1.795526740922480e+00 -1.384818405289922e-02 0.000000000000000e+00
|
||||
2.950000000000000e-01 -2.270711222931410e-01 -1.319968228007472e+00 1.793877417528653e+00 -1.235548207917668e-02 0.000000000000000e+00
|
||||
3.000000000000000e-01 -1.059952406492379e-01 -1.334571432743453e+00 1.792315900135202e+00 -1.089262568005408e-02 0.000000000000000e+00
|
||||
3.050000000000000e-01 1.586788096986941e-02 -1.338130490110278e+00 1.790844998209246e+00 -9.643946760528127e-03 0.000000000000000e+00
|
||||
3.100000000000001e-01 1.375137265470349e-01 -1.330622667417959e+00 1.789466708035337e+00 -8.390058535415246e-03 0.000000000000000e+00
|
||||
3.150000000000001e-01 2.579401191174317e-01 -1.312116267671406e+00 1.788182204938256e+00 -7.263771941028431e-03 0.000000000000000e+00
|
||||
3.200000000000000e-01 3.761554302435599e-01 -1.282770022974591e+00 1.786991839543951e+00 -6.241881151896921e-03 0.000000000000000e+00
|
||||
3.250000000000001e-01 4.911867003871064e-01 -1.242831751891369e+00 1.785895138146543e+00 -5.326178754556312e-03 0.000000000000000e+00
|
||||
3.300000000000000e-01 6.020876046455261e-01 -1.192636291738931e+00 1.784890808040575e+00 -4.535106936238389e-03 0.000000000000000e+00
|
||||
3.350000000000001e-01 7.079461995323322e-01 -1.132602722302246e+00 1.783976747998731e+00 -3.878329685474962e-03 0.000000000000000e+00
|
||||
3.400000000000000e-01 8.078923880921655e-01 -1.063230903250780e+00 1.783150064364732e+00 -3.354566468273623e-03 0.000000000000000e+00
|
||||
3.450000000000000e-01 9.011050428430696e-01 -9.850973530888535e-01 1.782407093299875e+00 -2.961302511327530e-03 0.000000000000000e+00
|
||||
3.500000000000000e-01 9.868187287166792e-01 -8.988505027676712e-01 1.781743429671698e+00 -2.700068018210533e-03 0.000000000000000e+00
|
||||
3.550000000000000e-01 1.064329971285002e+00 -8.052053621393731e-01 1.781153962993531e+00 -2.573382140259873e-03 0.000000000000000e+00
|
||||
3.600000000000000e-01 1.133003019121349e+00 -7.049376422246523e-01 1.780632920763343e+00 -2.579663820909457e-03 0.000000000000000e+00
|
||||
3.650000000000000e-01 1.192275053141959e+00 -5.988773807457668e-01 1.780173919513572e+00 -2.712782869197503e-03 0.000000000000000e+00
|
||||
3.700000000000000e-01 1.241660800186358e+00 -4.879021224839045e-01 1.779770023843727e+00 -2.965987008367172e-03 0.000000000000000e+00
|
||||
3.750000000000001e-01 1.280756512865674e+00 -3.729297097065013e-01 1.779413813629617e+00 -3.333831145550517e-03 0.000000000000000e+00
|
||||
3.800000000000000e-01 1.309243282782769e+00 -2.549107411562341e-01 1.779097459468623e+00 -3.807949202540237e-03 0.000000000000000e+00
|
||||
3.850000000000001e-01 1.326889659571054e+00 -1.348207608954150e-01 1.778812806245006e+00 -4.373286143067137e-03 0.000000000000000e+00
|
||||
3.900000000000001e-01 1.333553553802217e+00 -1.365224063699080e-02 1.778551464532933e+00 -5.018175080135233e-03 0.000000000000000e+00
|
||||
3.950000000000000e-01 1.329183407667964e+00 1.075935790047660e-01 1.778304909462876e+00 -5.745887933107595e-03 0.000000000000000e+00
|
||||
4.000000000000000e-01 1.313818623354443e+00 2.279149217599039e-01 1.778064586633785e+00 -6.554798061470132e-03 0.000000000000000e+00
|
||||
4.050000000000000e-01 1.287589245026442e+00 3.463177160572142e-01 1.777822024362848e+00 -7.319459393699334e-03 0.000000000000000e+00
|
||||
4.100000000000001e-01 1.250714896209305e+00 4.618237747552283e-01 1.777568950529021e+00 -8.168006008658336e-03 0.000000000000000e+00
|
||||
4.150000000000000e-01 1.203502981174627e+00 5.734788474155926e-01 1.777297414129333e+00 -9.000207340362451e-03 0.000000000000000e+00
|
||||
4.200000000000000e-01 1.146346164161466e+00 6.803604786069781e-01 1.776999908938022e+00 -9.822174334662566e-03 0.000000000000000e+00
|
||||
4.250000000000000e-01 1.079719146923773e+00 7.815856079680715e-01 1.776669498816621e+00 -1.062476276463385e-02 0.000000000000000e+00
|
||||
4.300000000000000e-01 1.004174770272181e+00 8.763178488692061e-01 1.776299941497941e+00 -1.137795205096321e-02 0.000000000000000e+00
|
||||
4.350000000000001e-01 9.203394715174532e-01 9.637743859448440e-01 1.775885809836386e+00 -1.205529098227613e-02 0.000000000000000e+00
|
||||
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|
||||
2.605000000000000e+00 -1.198422697631716e+00 5.747229984613373e-01 1.766523487159269e+00 8.587600763253125e-03 1.626193911082762e-06
|
||||
2.609999999999999e+00 -1.246098257390493e+00 4.630718501924150e-01 1.767196405512249e+00 8.528025902488181e-03 1.461948498278889e-06
|
||||
2.614999999999999e+00 -1.283402806071555e+00 3.475218190592554e-01 1.767894177354594e+00 8.427526331449440e-03 1.269366915141029e-06
|
||||
2.619999999999999e+00 -1.310020762419759e+00 2.290328060586587e-01 1.768610424221949e+00 8.297687762092568e-03 1.019515064317471e-06
|
||||
2.625000000000000e+00 -1.325725133299823e+00 1.085898214632856e-01 1.769338878388261e+00 8.154633163539149e-03 7.304448226595559e-07
|
||||
2.629999999999999e+00 -1.330379482874979e+00 -1.280516784417712e-02 1.770073540778216e+00 8.007815723604265e-03 4.286648254627381e-07
|
||||
2.634999999999999e+00 -1.323939153839033e+00 -1.341415418137323e-01 1.770808836308179e+00 7.865129157565234e-03 1.558109867937735e-07
|
||||
2.640000000000000e+00 -1.306451729338362e+00 -2.544084132067350e-01 1.771539761801565e+00 7.740213015982873e-03 -1.716944673716187e-07
|
||||
2.644999999999999e+00 -1.278056730183839e+00 -3.726030268498164e-01 1.772262021185850e+00 7.650638876039855e-03 -5.073591211890336e-07
|
||||
2.649999999999999e+00 -1.238984548431687e+00 -4.877391024536233e-01 1.772972143314738e+00 7.610202088129870e-03 -8.359413321903563e-07
|
||||
2.654999999999999e+00 -1.189554624942858e+00 -5.988550516515878e-01 1.773667578611569e+00 7.624994685630567e-03 -1.143334407668656e-06
|
||||
2.659999999999999e+00 -1.130172884823164e+00 -7.050220009472276e-01 1.774346771409145e+00 7.697941106455705e-03 -1.460293348508732e-06
|
||||
2.664999999999999e+00 -1.061328450691569e+00 -8.053515537468765e-01 1.775009205369874e+00 7.836711590093503e-03 -1.736983116247982e-06
|
||||
2.669999999999999e+00 -9.835896596579697e-01 -8.990032265470798e-01 1.775655419928141e+00 8.054911824959422e-03 -1.977211347462761e-06
|
||||
2.674999999999999e+00 -8.975994157870431e-01 -9.851914967710838e-01 1.776286996531290e+00 8.362067170068290e-03 -2.214615401648293e-06
|
||||
2.679999999999999e+00 -8.040699155592210e-01 -1.063192402867803e+00 1.776906514623226e+00 8.751893795480638e-03 -2.413941112071185e-06
|
||||
2.685000000000000e+00 -7.037767891555129e-01 -1.132349641083667e+00 1.777517478616353e+00 9.208641341460691e-03 -2.557486265718394e-06
|
||||
2.690000000000000e+00 -5.975527051370131e-01 -1.192080107506443e+00 1.778124218129135e+00 9.738061962761273e-03 -2.649052584852429e-06
|
||||
2.694999999999999e+00 -4.862804905304253e-01 -1.241878838155088e+00 1.778731764127942e+00 1.037078866462557e-02 -2.678540106211125e-06
|
||||
2.699999999999999e+00 -3.708858233302778e-01 -1.281323304035184e+00 1.779345703411018e+00 1.110850376006232e-02 -2.697512969470784e-06
|
||||
2.705000000000000e+00 -2.523295569629781e-01 -1.310077025117729e+00 1.779972017058451e+00 1.175997526136203e-02 -2.642205515919498e-06
|
||||
2.709999999999999e+00 -1.315997404852944e-01 -1.327892471808312e+00 1.780616908380984e+00 1.255722899226111e-02 -2.521118383817418e-06
|
||||
2.714999999999999e+00 -9.703400165999410e-03 -1.334613227564892e+00 1.781286623165960e+00 1.335746136815370e-02 -2.369283591660143e-06
|
||||
2.719999999999999e+00 1.123418489349637e-01 -1.330175394119143e+00 1.781987270142144e+00 1.418217524664051e-02 -2.148662530487710e-06
|
||||
2.724999999999999e+00 2.335162921416328e-01 -1.314608225215903e+00 1.782724644500883e+00 1.502493098320280e-02 -1.886064456691688e-06
|
||||
2.729999999999999e+00 3.528066335028148e-01 -1.288033983195452e+00 1.783504062509931e+00 1.585804232881888e-02 -1.590981676487163e-06
|
||||
2.734999999999999e+00 4.692144727727885e-01 -1.250667017523023e+00 1.784330210179380e+00 1.666142133218636e-02 -1.267091524275591e-06
|
||||
2.739999999999999e+00 5.817646697569806e-01 -1.202812071429551e+00 1.785207010154096e+00 1.742695760254412e-02 -8.822757897207890e-07
|
||||
2.744999999999999e+00 6.895135255735770e-01 -1.144861829625894e+00 1.786137510883252e+00 1.814801704787986e-02 -4.929508160457936e-07
|
||||
2.750000000000000e+00 7.915567119642350e-01 -1.077293726375905e+00 1.787123801144515e+00 1.881231314382626e-02 -6.329303372606262e-08
|
||||
2.754999999999999e+00 8.870368817634086e-01 -1.000666039275165e+00 1.788166951767197e+00 1.940458164333563e-02 3.460610549468852e-07
|
||||
2.759999999999999e+00 9.751508960327387e-01 -9.156133000827225e-01 1.789266985321827e+00 1.991336700504602e-02 7.741986391809734e-07
|
||||
2.764999999999999e+00 1.055156606356244e+00 -8.228410598777476e-01 1.790422873757961e+00 2.033356366221517e-02 1.181378757084515e-06
|
||||
2.769999999999999e+00 1.126379134452799e+00 -7.231200514664610e-01 1.791632563363493e+00 2.066264920366536e-02 1.617805771107035e-06
|
||||
2.774999999999999e+00 1.188216595487887e+00 -6.172797971448853e-01 1.792893025756056e+00 2.089642306190662e-02 2.007534359693527e-06
|
||||
2.779999999999999e+00 1.240145216048681e+00 -5.062017145820150e-01 1.794200332734203e+00 2.103092900140074e-02 2.357779627768280e-06
|
||||
2.784999999999999e+00 1.281723802567179e+00 -3.908117778592694e-01 1.795549751780791e+00 2.106802510399977e-02 2.675144026336082e-06
|
||||
2.789999999999999e+00 1.312597521175590e+00 -2.720727947264807e-01 1.796935858226581e+00 2.101169191506518e-02 2.979052177907127e-06
|
||||
2.794999999999999e+00 1.332500955928790e+00 -1.509763647503530e-01 1.798352660264371e+00 2.085630495149243e-02 3.218556549081505e-06
|
||||
2.799999999999999e+00 1.341260419274167e+00 -2.853458547598937e-02 1.799793734879801e+00 2.059548414016388e-02 3.402210785417331e-06
|
||||
2.804999999999999e+00 1.338795493081434e+00 9.422842379519958e-02 1.801252368146087e+00 2.031255594096269e-02 3.570643074704283e-06
|
||||
2.809999999999999e+00 1.325119786106040e+00 2.162851093736147e-01 1.802721696066472e+00 1.991543712230914e-02 3.639355255106677e-06
|
||||
2.814999999999999e+00 1.300340900887318e+00 3.366131091258347e-01 1.804194843755804e+00 1.947237527027509e-02 3.655122995044156e-06
|
||||
2.819999999999999e+00 1.264659608540402e+00 4.542038444004533e-01 1.805665057741716e+00 1.897505855368049e-02 3.629471727277381e-06
|
||||
2.824999999999999e+00 1.218368237757429e+00 5.680710048604332e-01 1.807125829339284e+00 1.842538685190026e-02 3.560497024998093e-06
|
||||
2.829999999999999e+00 1.161848290082099e+00 6.772588547543716e-01 1.808571005509900e+00 1.784312334203752e-02 3.430259774903017e-06
|
||||
2.834999999999999e+00 1.095567300842551e+00 7.808502896375775e-01 1.809994885502520e+00 1.724609935318650e-02 3.204824750798043e-06
|
||||
2.839999999999999e+00 1.020074971414046e+00 8.779745750557915e-01 1.811392301749764e+00 1.664027484969032e-02 2.957134160348685e-06
|
||||
2.844999999999999e+00 9.359986045842990e-01 9.678147012912501e-01 1.812758683819226e+00 1.602637190823196e-02 2.675928548300559e-06
|
||||
2.849999999999999e+00 8.440378808136820e-01 1.049614291314199e+00 1.814090104779460e+00 1.541081980875256e-02 2.335954071594933e-06
|
||||
2.854999999999999e+00 7.449590189683013e-01 1.122684002758327e+00 1.815383309991673e+00 1.480806006072861e-02 1.960879882593088e-06
|
||||
2.859999999999999e+00 6.395883704746561e-01 1.186407369019868e+00 1.816635728911072e+00 1.423229271555361e-02 1.571179611893852e-06
|
||||
2.864999999999999e+00 5.288055007194272e-01 1.240246029338876e+00 1.817845470881972e+00 1.368794015256541e-02 1.145460444909257e-06
|
||||
2.869999999999999e+00 4.135358159132408e-01 1.283744302856180e+00 1.819011306158729e+00 1.317007354771924e-02 6.709575612381225e-07
|
||||
2.874999999999999e+00 2.947427975971038e-01 1.316533067130548e+00 1.820132633583536e+00 1.267647496216467e-02 2.284333017855570e-07
|
||||
2.879999999999999e+00 1.734199104716843e-01 1.338332907487584e+00 1.821209436612178e+00 1.221844128688177e-02 -2.132823422438609e-07
|
||||
2.884999999999999e+00 5.058225216434278e-02 1.348956509856380e+00 1.822242229717923e+00 1.181156429544282e-02 -6.667567430686481e-07
|
||||
2.889999999999999e+00 -7.274198421521169e-02 1.348310276306393e+00 1.823231997460986e+00 1.144622007963591e-02 -1.131293186120537e-06
|
||||
2.894999999999999e+00 -1.955201623343889e-01 1.336395149056922e+00 1.824180128302139e+00 1.109000219439828e-02 -1.584461768433070e-06
|
||||
2.899999999999999e+00 -3.167238961530268e-01 1.313306635043235e+00 1.825088344042939e+00 1.073795934643945e-02 -1.974061293797740e-06
|
||||
2.904999999999999e+00 -4.353377106257118e-01 1.279234030861210e+00 1.825958628006257e+00 1.053410796731755e-02 -2.379475006095768e-06
|
||||
2.909999999999999e+00 -5.503675959366392e-01 1.234458854301034e+00 1.826793153619298e+00 1.027883646506820e-02 -2.746169779917936e-06
|
||||
2.914999999999999e+00 -6.608493824260464e-01 1.179352495190617e+00 1.827594214165221e+00 1.007128012026653e-02 -3.060914722984974e-06
|
||||
2.919999999999999e+00 -7.658568647929271e-01 1.114373105618383e+00 1.828364155876013e+00 9.880847359467653e-03 -3.365624669574133e-06
|
||||
2.924999999999999e+00 -8.645096064263889e-01 1.040061755631267e+00 1.829105315130303e+00 9.699328813425986e-03 -3.633183866418347e-06
|
||||
2.929999999999999e+00 -9.559803572641514e-01 9.570378871850806e-01 1.829819960982578e+00 9.530693956559233e-03 -3.845587518351549e-06
|
||||
2.934999999999999e+00 -1.039502022088382e+00 8.659941049020907e-01 1.830510243651009e+00 9.372019062387528e-03 -3.984902253429147e-06
|
||||
2.939999999999999e+00 -1.114374119901103e+00 7.676903479718018e-01 1.831178149474425e+00 9.214317180289014e-03 -4.122735600345433e-06
|
||||
2.944999999999999e+00 -1.179968679407875e+00 6.629474928887277e-01 1.831825462711015e+00 9.050236532309472e-03 -4.201034651386331e-06
|
||||
2.949999999999999e+00 -1.235735520522679e+00 5.526404415901718e-01 1.832453734362437e+00 8.876186285861027e-03 -4.248418948202105e-06
|
||||
2.954999999999999e+00 -1.281206877097457e+00 4.376907539353904e-01 1.833064258002348e+00 8.688768257735006e-03 -4.220892120591392e-06
|
||||
2.959999999999999e+00 -1.316001321737907e+00 3.190588873505835e-01 1.833658052413309e+00 8.482226730828438e-03 -4.174545810386011e-06
|
||||
2.964999999999999e+00 -1.339826959568939e+00 1.977361098224936e-01 1.834235850715481e+00 8.250793979015146e-03 -4.065316758649098e-06
|
||||
2.969999999999999e+00 -1.352483864118988e+00 7.473615520455733e-02 1.834798095596991e+00 7.992452274044517e-03 -3.943687384413561e-06
|
||||
2.974999999999999e+00 -1.353865735032848e+00 -4.891330803841645e-02 1.835344940199295e+00 7.707385031563421e-03 -3.781601310095323e-06
|
||||
2.979999999999999e+00 -1.343960764016369e+00 -1.721793219971568e-01 1.835876254138862e+00 7.390729825484584e-03 -3.576680530427209e-06
|
||||
2.984999999999999e+00 -1.322851702194330e+00 -2.940323248462684e-01 1.836391634052937e+00 7.031500599447542e-03 -3.336245112093739e-06
|
||||
2.989999999999999e+00 -1.290715128891834e+00 -4.134548028927609e-01 1.836890417985356e+00 6.630894624587497e-03 -3.086278449398003e-06
|
||||
2.994999999999999e+00 -1.247819928723575e+00 -5.294498356449761e-01 1.837371702984198e+00 6.212872331271471e-03 -2.792923518764128e-06
|
||||
1206
figs/current.fig/mc18.dat
Normal file
1206
figs/current.fig/mc18.dat
Normal file
File diff suppressed because it is too large
Load Diff
1206
figs/current.fig/mc30.dat
Normal file
1206
figs/current.fig/mc30.dat
Normal file
File diff suppressed because it is too large
Load Diff
32
figs/omega.fig/Makefile
Normal file
32
figs/omega.fig/Makefile
Normal file
@ -0,0 +1,32 @@
|
||||
PROJECTNAME=omega
|
||||
|
||||
PHOTOCOMP_PATH=
|
||||
|
||||
DATS=omega.dat
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(DATS)
|
||||
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
omega.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega_min=5;omega_max=6;n_omega=50;n_periods=12;J=120;E=10e9" mc_avgavgcurrent_omega > $@
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-dat:
|
||||
rm -f $(DATS)
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
|
||||
clean: clean-aux clean-tex
|
||||
57
figs/omega.fig/omega.dat
Normal file
57
figs/omega.fig/omega.dat
Normal file
@ -0,0 +1,57 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.549800000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=4.570246362361185, E=1.000000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=2.813332376726366e-01 omega=1.549800000000000e-01 m=1.000000000000000e+00, keldysh=1.863997401882817e+00
|
||||
#numerical precision (matching): n_periods=12 NC=12 gl_order=16 J0=1 J=120
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
# omega n_photons avgavgcurrent mu_t M_t
|
||||
|
||||
5.000000000000000e+00 1.115208395170143e+00 -1.767254374839443e-06 -5.872759586088563e-06 3.688215275613987e-06
|
||||
5.020408163265307e+00 1.110552135135230e+00 3.481769195644922e-06 -9.520100843546093e-07 9.255081504239878e-06
|
||||
5.040816326530612e+00 1.105935061178769e+00 8.694844819654358e-06 3.995239195851555e-06 1.275579751852944e-05
|
||||
5.061224489795919e+00 1.101356675491701e+00 8.799345752084708e-06 3.933492541232696e-06 1.224640794826752e-05
|
||||
5.081632653061225e+00 1.096816488736612e+00 3.536546271238413e-06 -1.397979335805772e-06 8.522746047746839e-06
|
||||
5.102040816326531e+00 1.092314019866977e+00 -2.678873432257001e-06 -7.040626921087629e-06 2.405571404876937e-06
|
||||
5.122448979591836e+00 1.087848795951036e+00 -4.141432277868735e-06 -8.179726614834721e-06 8.328635003936747e-07
|
||||
5.142857142857143e+00 1.083420352000169e+00 1.065329962725955e-06 -3.219042681999279e-06 7.194092044434094e-06
|
||||
5.163265306122449e+00 1.079028230801629e+00 8.827945387434261e-06 3.894608130034307e-06 1.361133448724558e-05
|
||||
5.183673469387755e+00 1.074671982755515e+00 1.183484927813807e-05 6.720377263410872e-06 1.480764494759398e-05
|
||||
5.204081632653061e+00 1.070351165715842e+00 7.157858272739758e-06 2.032275766979137e-06 1.184457809771067e-05
|
||||
5.224489795918367e+00 1.066065344835611e+00 -1.780531480642952e-06 -6.314231515448376e-06 3.710341161754937e-06
|
||||
5.244897959183675e+00 1.061814092415737e+00 -6.974014215351573e-06 -1.081260460372574e-05 -2.354147606942842e-06
|
||||
5.265306122448980e+00 1.057596987757747e+00 -2.919310525570610e-06 -6.939018900602607e-06 3.261584855438926e-06
|
||||
5.285714285714286e+00 1.053413617020115e+00 7.805288821933059e-06 2.919606326911266e-06 1.322079040879357e-05
|
||||
5.306122448979592e+00 1.049263573078148e+00 1.604608685234645e-05 1.091547032847531e-05 1.965592004543567e-05
|
||||
5.326530612244898e+00 1.045146455387307e+00 1.342844042504459e-05 8.070509203493191e-06 1.742760293516599e-05
|
||||
5.346938775510203e+00 1.041061869849881e+00 6.319329527833020e-07 -4.136336829806877e-06 6.406676540427386e-06
|
||||
5.367346938775510e+00 1.037009428684893e+00 -1.134767642351268e-05 -1.506771058349229e-05 -5.844979965672390e-06
|
||||
5.387755102040817e+00 1.032988750301173e+00 -1.067393364549286e-05 -1.421962846406221e-05 -4.722030737635214e-06
|
||||
5.408163265306122e+00 1.028999459173493e+00 5.215086717154612e-06 6.836825598078386e-07 1.134663037774954e-05
|
||||
5.428571428571429e+00 1.025041185721677e+00 2.441354215520772e-05 1.886703947235648e-05 2.858626902354553e-05
|
||||
5.448979591836735e+00 1.021113566192615e+00 2.822567366351067e-05 2.215698191711490e-05 3.098415058909033e-05
|
||||
5.469387755102041e+00 1.017216242545081e+00 6.863535715779913e-06 1.809450344973610e-06 1.214526030149579e-05
|
||||
5.489795918367346e+00 1.013348862337299e+00 -2.727525178415409e-05 -3.065256869035489e-05 -2.028636911037119e-05
|
||||
5.510204081632653e+00 1.009511078617158e+00 -4.093113725581106e-05 -4.323799845384540e-05 -3.387376664678247e-05
|
||||
5.530612244897959e+00 1.005702549815022e+00 3.817865286531565e-06 -5.142462430566329e-07 9.578586005080775e-06
|
||||
5.551020408163265e+00 1.001922939639051e+00 1.261566938428398e-04 1.153817323932535e-04 1.255952555714206e-04
|
||||
5.571428571428571e+00 9.981719169729742e-01 3.136578059083432e-04 2.930605844124897e-04 3.021841533407623e-04
|
||||
5.591836734693878e+00 9.944491557762352e-01 5.259860824154864e-04 4.944117334814721e-04 5.042492984297921e-04
|
||||
5.612244897959185e+00 9.907543349864588e-01 7.164148553233928e-04 6.751394677101236e-04 6.854066404094009e-04
|
||||
5.632653061224490e+00 9.870871384241715e-01 8.537858911063791e-04 8.058221638153582e-04 8.150518511841755e-04
|
||||
5.653061224489796e+00 9.834472546997073e-01 9.353257382948215e-04 8.829420577167401e-04 8.927529991862424e-04
|
||||
5.673469387755102e+00 9.798343771222539e-01 9.817646019054812e-04 9.270353579757282e-04 9.371733789868266e-04
|
||||
5.693877551020408e+00 9.762482036109686e-01 1.018946634135041e-03 9.621784532074163e-04 9.716817519431893e-04
|
||||
5.714285714285714e+00 9.726884366081232e-01 1.062632861711127e-03 1.003323643755882e-03 1.013021944472856e-03
|
||||
5.734693877551020e+00 9.691547829942048e-01 1.112490823467546e-03 1.050680221296718e-03 1.060895473227898e-03
|
||||
5.755102040816327e+00 9.656469540049427e-01 1.158259765555210e-03 1.094279665056827e-03 1.104186194449871e-03
|
||||
5.775510204081632e+00 9.621646651501934e-01 1.191371799970765e-03 1.126273990852587e-03 1.135056870744205e-03
|
||||
5.795918367346939e+00 9.587076361346428e-01 1.211442176666135e-03 1.145140636162794e-03 1.154860889304104e-03
|
||||
5.816326530612245e+00 9.552755907802787e-01 1.225889650553572e-03 1.158509079321945e-03 1.168174717175902e-03
|
||||
5.836734693877551e+00 9.518682569505817e-01 1.242507899351386e-03 1.174196719688448e-03 1.183717652034037e-03
|
||||
5.857142857142856e+00 9.484853664763989e-01 1.263551131600086e-03 1.194064607016431e-03 1.204602932412491e-03
|
||||
5.877551020408164e+00 9.451266550834464e-01 1.285371822702834e-03 1.215127891243085e-03 1.225267717535952e-03
|
||||
5.897959183673469e+00 9.417918623214092e-01 1.301870093180957e-03 1.230772703738859e-03 1.240099864845858e-03
|
||||
5.918367346938775e+00 9.384807314945884e-01 1.311323970089323e-03 1.239871121117092e-03 1.249887264888310e-03
|
||||
5.938775510204081e+00 9.351930095940618e-01 1.316437740598745e-03 1.244633452909735e-03 1.254030609123569e-03
|
||||
5.959183673469388e+00 9.319284472313192e-01 1.321803385993161e-03 1.249587109594438e-03 1.258853111919532e-03
|
||||
5.979591836734695e+00 9.286867985733309e-01 1.330167086142919e-03 1.257309860267525e-03 1.267423484293473e-03
|
||||
6.000000000000000e+00 9.254678212790179e-01 1.340116024296602e-03 1.266994280781395e-03 1.277256236322942e-03
|
||||
22
figs/omega.fig/omega.gnuplot
Normal file
22
figs/omega.fig/omega.gnuplot
Normal file
@ -0,0 +1,22 @@
|
||||
set ylabel "$\\frac1k\\left<\\left<j\\right>\\right>$" norotate offset -1,0
|
||||
set xlabel "$\\omega (\\mathrm{eV})$"
|
||||
|
||||
set xtics 5,0.25
|
||||
set ytics 0,0.0005
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot "omega.dat" using 1:3 with lines linestyle 1
|
||||
32
figs/wavefunction.fig/Makefile
Normal file
32
figs/wavefunction.fig/Makefile
Normal file
@ -0,0 +1,32 @@
|
||||
PROJECTNAME=real imag density current
|
||||
|
||||
PHOTOCOMP_PATH=
|
||||
|
||||
DATS=mc.dat
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(DATS)
|
||||
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
mc.dat:
|
||||
$(PHOTOCOMP_PATH)photocomp -p "V=10;EF=4.5;omega=1.55;n_periods=3;J=30;E=15e9" mc > $@
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-dat:
|
||||
rm -f $(DATS)
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
|
||||
clean: clean-aux clean-tex
|
||||
28
figs/wavefunction.fig/current.gnuplot
Normal file
28
figs/wavefunction.fig/current.gnuplot
Normal file
@ -0,0 +1,28 @@
|
||||
set ylabel "$\\frac jk$" norotate
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,1
|
||||
set ytics -0.3,0.15
|
||||
|
||||
set yrange [-0.3:0.3]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
set label "\\bf (d)" at 2.65,0.28
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot cos(2*pi*x) axes x1y2 linetype 0 linewidth 2 ,\
|
||||
"mc.dat" using 1:5 with lines linestyle 1
|
||||
28
figs/wavefunction.fig/density.gnuplot
Normal file
28
figs/wavefunction.fig/density.gnuplot
Normal file
@ -0,0 +1,28 @@
|
||||
set ylabel "$|\\psi_0|^2$" offset -1
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,1
|
||||
set ytics 1.6,0.1
|
||||
|
||||
set yrange [1.6:2]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
set label "\\bf (c)" at 2.65,1.987
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot cos(2*pi*x) axes x1y2 linetype 0 linewidth 2 ,\
|
||||
"mc.dat" using 1:4 with lines linestyle 2
|
||||
28
figs/wavefunction.fig/imag.gnuplot
Normal file
28
figs/wavefunction.fig/imag.gnuplot
Normal file
@ -0,0 +1,28 @@
|
||||
set ylabel "$\\mathcal Im(e^{\\frac{ik^2}2t}\\psi_0)$" offset -1
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,1
|
||||
set ytics -1.02, 0.02
|
||||
|
||||
set yrange [-1.02:-0.94]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
set label "\\bf (b)" at 2.65,-0.943
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot cos(2*pi*x) axes x1y2 linetype 0 linewidth 2 ,\
|
||||
"mc.dat" using 1:3 with lines linestyle 5
|
||||
606
figs/wavefunction.fig/mc.dat
Normal file
606
figs/wavefunction.fig/mc.dat
Normal file
@ -0,0 +1,606 @@
|
||||
#parameters: V_=1.000000000000000e+01 eV, EF=4.500000000000000e+00 eV, omega_=1.550000000000000e+00 eV, theta= 0.000000000000000e+00*pi W=5.500000000000000e+00 eV, n_photons=5.845650641658291, E=1.500000000000000e+10 V/m
|
||||
#dimensionless: V=1.000000000000000e+00 k=9.486832980505138e-01 epsilon=4.219454049145666e-01 omega=1.550000000000000e-01 m=1.000000000000000e+00, keldysh=1.242825299143273e+00
|
||||
#numerical precision (matching): n_periods=3 NC=12 gl_order=16 J0=1 J=30
|
||||
#numerical precision (Crank-Nicolson): bmin=-2.000000000000000e+02 bmax= 2.000000000000000e+02 nx_cn=4000 mu= 1.000000000000000e-01
|
||||
#
|
||||
#% t real(psi0) imag(psi0) abs(psi0)^2 current avgcurrent
|
||||
|
||||
5.000000000000000e-03 9.011237076219065e-01 -9.920990592322099e-01 1.796284479767687e+00 4.066156482056959e-02 0.000000000000000e+00
|
||||
1.000000000000000e-02 9.036959786184608e-01 -9.882977598906416e-01 1.793398883976038e+00 7.201570001853567e-02 0.000000000000000e+00
|
||||
1.500000000000000e-02 9.071741251355965e-01 -9.846371696331014e-01 1.792475249138620e+00 9.663201291162658e-02 0.000000000000000e+00
|
||||
2.000000000000000e-02 9.112296705251185e-01 -9.813857962466512e-01 1.793457593519989e+00 1.156836312659321e-01 0.000000000000000e+00
|
||||
2.500000000000000e-02 9.156315488882216e-01 -9.786363650543179e-01 1.796110268326171e+00 1.300140368375609e-01 0.000000000000000e+00
|
||||
3.000000000000000e-02 9.202092406537398e-01 -9.764097761814351e-01 1.800161097607213e+00 1.403024957858335e-01 0.000000000000000e+00
|
||||
3.500000000000000e-02 9.248342007156113e-01 -9.746926619406401e-01 1.805344084054215e+00 1.471214533034481e-01 0.000000000000000e+00
|
||||
4.000000000000000e-02 9.294087151999519e-01 -9.734546205103959e-01 1.811414458082664e+00 1.509624712076890e-01 0.000000000000000e+00
|
||||
4.500000000000001e-02 9.338584744101831e-01 -9.726571105729394e-01 1.818153504975813e+00 1.522511450122389e-01 0.000000000000000e+00
|
||||
5.000000000000000e-02 9.381272651449116e-01 -9.722583413438044e-01 1.825369047920877e+00 1.513577520549300e-01 0.000000000000000e+00
|
||||
5.500000000000001e-02 9.421730056725623e-01 -9.722160593995715e-01 1.832894038772501e+00 1.486057844547027e-01 0.000000000000000e+00
|
||||
6.000000000000000e-02 9.459647126258931e-01 -9.724891675652013e-01 1.840584418565047e+00 1.442788734682609e-01 0.000000000000000e+00
|
||||
6.500000000000002e-02 9.494801620644853e-01 -9.730386635010360e-01 1.848316818821883e+00 1.386261574576297e-01 0.000000000000000e+00
|
||||
6.999999999999999e-02 9.527040875297279e-01 -9.738281577164219e-01 1.855986359157212e+00 1.318662195761259e-01 0.000000000000000e+00
|
||||
7.500000000000001e-02 9.556267922545760e-01 -9.748241117959209e-01 1.863504615013477e+00 1.241900105915355e-01 0.000000000000000e+00
|
||||
8.000000000000000e-02 9.582430653714695e-01 -9.759958802677270e-01 1.870797730632085e+00 1.157634999719579e-01 0.000000000000000e+00
|
||||
8.499999999999999e-02 9.605512976454061e-01 -9.773156201123415e-01 1.877804616723844e+00 1.067310507759197e-01 0.000000000000000e+00
|
||||
9.000000000000001e-02 9.625527002638457e-01 -9.787581363206964e-01 1.884475190199185e+00 9.722061483045315e-02 0.000000000000000e+00
|
||||
9.500000000000000e-02 9.642505464632329e-01 -9.803007501840784e-01 1.890768677166111e+00 8.735174630418781e-02 0.000000000000000e+00
|
||||
1.000000000000000e-01 9.656494720497791e-01 -9.819232614121206e-01 1.896652194172233e+00 7.717084793097032e-02 0.000000000000000e+00
|
||||
1.050000000000000e-01 9.667560119471850e-01 -9.836073909573243e-01 1.902100686181900e+00 6.692255162050811e-02 0.000000000000000e+00
|
||||
1.100000000000000e-01 9.675773401526806e-01 -9.853368961697180e-01 1.907094708130310e+00 5.649691266971005e-02 0.000000000000000e+00
|
||||
1.150000000000000e-01 9.681214356722894e-01 -9.870972382756389e-01 1.911620072019568e+00 4.606200814956234e-02 0.000000000000000e+00
|
||||
1.200000000000000e-01 9.683968104664674e-01 -9.888754153785958e-01 1.915666969661818e+00 3.564877803455044e-02 0.000000000000000e+00
|
||||
1.250000000000000e-01 9.684123506055112e-01 -9.906597829122454e-01 1.919229286285029e+00 2.530114137575188e-02 0.000000000000000e+00
|
||||
1.300000000000000e-01 9.681771924255469e-01 -9.924398857564037e-01 1.922304002773198e+00 1.507822506166007e-02 0.000000000000000e+00
|
||||
1.350000000000000e-01 9.677006277490590e-01 -9.942063027588171e-01 1.924890677391279e+00 5.028811658825997e-03 0.000000000000000e+00
|
||||
1.400000000000000e-01 9.669920332627706e-01 -9.959505039872319e-01 1.926990998786089e+00 -4.815552690807036e-03 0.000000000000000e+00
|
||||
1.450000000000000e-01 9.660608199938793e-01 -9.976647207498106e-01 1.928608402956044e+00 -1.442979143403208e-02 0.000000000000000e+00
|
||||
1.500000000000000e-01 9.649163995205725e-01 -9.993418282268303e-01 1.929747747707489e+00 -2.378406037313757e-02 0.000000000000000e+00
|
||||
1.550000000000000e-01 9.635681641175022e-01 -1.000975240429556e+00 1.930415038853780e+00 -3.284335335275433e-02 0.000000000000000e+00
|
||||
1.600000000000000e-01 9.620254784938809e-01 -1.002558817128361e+00 1.930617203073199e+00 -4.157586946041263e-02 0.000000000000000e+00
|
||||
1.650000000000000e-01 9.602976811523672e-01 -1.004086782359574e+00 1.930361902935817e+00 -4.995966941801407e-02 0.000000000000000e+00
|
||||
1.700000000000000e-01 9.583940936992136e-01 -1.005553654117106e+00 1.929657390145802e+00 -5.797950092919826e-02 0.000000000000000e+00
|
||||
1.750000000000000e-01 9.563240366834969e-01 -1.006954184848671e+00 1.928512393522870e+00 -6.561621121845297e-02 0.000000000000000e+00
|
||||
1.800000000000000e-01 9.540968507430752e-01 -1.008283312397738e+00 1.926936038657608e+00 -7.284090773107083e-02 0.000000000000000e+00
|
||||
1.850000000000000e-01 9.517219219909825e-01 -1.009536121056629e+00 1.924937796516275e+00 -7.962442670854655e-02 0.000000000000000e+00
|
||||
1.900000000000000e-01 9.492087106924261e-01 -1.010707812426299e+00 1.922527458553933e+00 -8.595458535847925e-02 0.000000000000000e+00
|
||||
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|
||||
2.924999999999999e+00 9.436650105595440e-01 -1.004145757306089e+00 1.898812354070164e+00 -1.214562192424584e-02 4.011942101974792e-05
|
||||
2.929999999999999e+00 9.434322187068021e-01 -1.002763830816105e+00 1.895599651687028e+00 -3.449015471118240e-03 3.898287685562010e-05
|
||||
2.934999999999999e+00 9.434380607721273e-01 -1.001249532516582e+00 1.892576000878148e+00 5.485895106727420e-03 3.794376249638483e-05
|
||||
2.939999999999999e+00 9.436794919629317e-01 -9.996502244732529e-01 1.889831554840842e+00 1.442253971405652e-02 3.697318438453617e-05
|
||||
2.944999999999999e+00 9.441471410967328e-01 -9.980090689848029e-01 1.887435925817047e+00 2.315425224457108e-02 3.613594196604455e-05
|
||||
2.949999999999999e+00 9.448265645747584e-01 -9.963645486484057e-01 1.885439550929482e+00 3.151559147416701e-02 3.538211138255486e-05
|
||||
2.954999999999999e+00 9.456994257772195e-01 -9.947502269815081e-01 1.883875417995125e+00 3.937811340328699e-02 3.478451610537384e-05
|
||||
2.959999999999999e+00 9.467445733191104e-01 -9.931947089279223e-01 1.882761016951605e+00 4.663885428564447e-02 3.428282467501702e-05
|
||||
2.964999999999999e+00 9.479390019138521e-01 -9.917217605286136e-01 1.882100401655403e+00 5.321412102780114e-02 3.391302714424924e-05
|
||||
2.969999999999999e+00 9.492586868921338e-01 -9.903505487954311e-01 1.881886264139589e+00 5.904238694283432e-02 3.359797860567006e-05
|
||||
2.974999999999999e+00 9.506792892252258e-01 -9.890959669316935e-01 1.882101942762323e+00 6.408840260766342e-02 3.342071335995561e-05
|
||||
2.979999999999999e+00 9.521767337989366e-01 -9.879690158146953e-01 1.882723308597869e+00 6.833843556032662e-02 3.335532641448861e-05
|
||||
2.984999999999999e+00 9.537276700345069e-01 -9.869772183405738e-01 1.883720498112746e+00 7.178899557659296e-02 3.338063211604125e-05
|
||||
2.989999999999999e+00 9.553098287718852e-01 -9.861250470424733e-01 1.885059477352689e+00 7.444714985380274e-02 3.345251436762203e-05
|
||||
2.994999999999999e+00 9.569022877989215e-01 -9.854143472756992e-01 1.886703424211602e+00 7.634448274519776e-02 3.362352834079004e-05
|
||||
28
figs/wavefunction.fig/real.gnuplot
Normal file
28
figs/wavefunction.fig/real.gnuplot
Normal file
@ -0,0 +1,28 @@
|
||||
set ylabel "$\\mathcal Re(e^{\\frac{ik^2}2t}\\psi_0)$" offset -1
|
||||
set xlabel "$\\frac{t\\omega}{2\\pi}$"
|
||||
|
||||
set xtics 0,1
|
||||
set ytics 0.82,0.04
|
||||
|
||||
set yrange [0.82:0.98]
|
||||
set y2range [-1.4:1.4]
|
||||
|
||||
# default output canvas size: 12.5cm x 8.75cm
|
||||
set term lua tikz size 8,6 standalone
|
||||
|
||||
# no key
|
||||
set key off
|
||||
|
||||
set label "\\bf (a)" at 2.65,0.974
|
||||
|
||||
# set linestyle
|
||||
set style line 1 linetype rgbcolor "#4169E1" linewidth 3
|
||||
set style line 2 linetype rgbcolor "#DC143C" linewidth 3
|
||||
set style line 3 linetype rgbcolor "#32CD32" linewidth 3
|
||||
set style line 4 linetype rgbcolor "#4B0082" linewidth 3
|
||||
set style line 5 linetype rgbcolor "#DAA520" linewidth 3
|
||||
|
||||
set pointsize 0.6
|
||||
|
||||
plot cos(2*pi*x) axes x1y2 linetype 0 linewidth 2 ,\
|
||||
"mc.dat" using 1:2 with lines linestyle 3
|
||||
673
libs/ian.cls
Normal file
673
libs/ian.cls
Normal file
@ -0,0 +1,673 @@
|
||||
%%
|
||||
%% Ian's class file
|
||||
%%
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% class name
|
||||
\ProvidesClass{ian}[2017/09/29]
|
||||
|
||||
%% boolean to signal that this class is being used
|
||||
\newif\ifianclass
|
||||
|
||||
%% options
|
||||
% no section numbering in equations
|
||||
\DeclareOption{section_in_eq}{\sectionsineqtrue}
|
||||
\DeclareOption{section_in_fig}{\sectionsinfigtrue}
|
||||
\DeclareOption{section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{section_in_all}{\sectionsineqtrue\sectionsinfigtrue\PassOptionsToPackage{section_in_theo}{iantheo}}
|
||||
\DeclareOption{subsection_in_eq}{\subsectionsineqtrue}
|
||||
\DeclareOption{subsection_in_fig}{\subsectionsinfigtrue}
|
||||
\DeclareOption{subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{subsection_in_all}{\subsectionsineqtrue\subsectionsinfigtrue\PassOptionsToPackage{subsection_in_theo}{iantheo}}
|
||||
\DeclareOption{no_section_in_eq}{\sectionsineqfalse}
|
||||
\DeclareOption{no_section_in_fig}{\sectionsinfigfalse}
|
||||
\DeclareOption{no_section_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{no_section_in_all}{\sectionsineqfalse\sectionsinfigfalse\PassOptionsToPackage{no_section_in_theo}{iantheo}}
|
||||
\DeclareOption{no_subsection_in_eq}{\subsectionsineqfalse}
|
||||
\DeclareOption{no_subsection_in_fig}{\subsectionsinfigfalse}
|
||||
\DeclareOption{no_subsection_in_theo}{\PassOptionsToPackage{\CurrentOption}{iantheo}}
|
||||
\DeclareOption{no_subsection_in_all}{\subsectionsineqfalse\subsectionsinfigfalse\PassOptionsToPackage{no_subsection_in_theo}{iantheo}}
|
||||
% reset point
|
||||
\DeclareOption{point_reset_at_section}{\PassOptionsToPackage{reset_at_section}{point}}
|
||||
\DeclareOption{point_no_reset_at_section}{\PassOptionsToPackage{no_reset_at_section}{point}}
|
||||
\DeclareOption{point_reset_at_theo}{\PassOptionsToPackage{reset_at_theo}{point}}
|
||||
\DeclareOption{point_no_reset_at_theo}{\PassOptionsToPackage{no_reset_at_theo}{point}}
|
||||
|
||||
\def\ian@defaultoptions{
|
||||
\ExecuteOptions{section_in_all, no_subsection_in_all}
|
||||
\ProcessOptions
|
||||
|
||||
%% required packages
|
||||
\RequirePackage{iantheo}
|
||||
\RequirePackage{point}
|
||||
\RequirePackage{color}
|
||||
\RequirePackage{marginnote}
|
||||
\RequirePackage{amssymb}
|
||||
\PassOptionsToPackage{hidelinks}{hyperref}
|
||||
\RequirePackage{hyperref}
|
||||
}
|
||||
|
||||
%% paper dimensions
|
||||
\setlength\paperheight{297mm}
|
||||
\setlength\paperwidth{210mm}
|
||||
|
||||
%% fonts
|
||||
\input{size11.clo}
|
||||
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
|
||||
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
|
||||
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
|
||||
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
|
||||
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
|
||||
|
||||
%% text dimensions
|
||||
\hoffset=-50pt
|
||||
\voffset=-72pt
|
||||
\textwidth=460pt
|
||||
\textheight=704pt
|
||||
|
||||
|
||||
%% remove default indentation
|
||||
\parindent=0pt
|
||||
%% indent command
|
||||
\def\indent{\hskip20pt}
|
||||
|
||||
%% something is wrong with \thepage, redefine it
|
||||
\gdef\thepage{\the\c@page}
|
||||
|
||||
%% array lines (to use the array environment)
|
||||
\setlength\arraycolsep{5\p@}
|
||||
\setlength\arrayrulewidth{.4\p@}
|
||||
|
||||
|
||||
%% correct vertical alignment at the end of a document
|
||||
\AtEndDocument{
|
||||
\vfill
|
||||
\eject
|
||||
}
|
||||
|
||||
|
||||
%% hyperlinks
|
||||
% hyperlinkcounter
|
||||
\newcounter{lncount}
|
||||
% hyperref anchor
|
||||
\def\hrefanchor{%
|
||||
\stepcounter{lncount}%
|
||||
\hypertarget{ln.\thelncount}{}%
|
||||
}
|
||||
|
||||
%% define a command and write it to aux file
|
||||
\def\outdef#1#2{%
|
||||
% define command%
|
||||
\expandafter\xdef\csname #1\endcsname{#2}%
|
||||
% hyperlink number%
|
||||
\expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
|
||||
% write command to aux%
|
||||
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
|
||||
\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
|
||||
}
|
||||
|
||||
%% can call commands even when they are not defined
|
||||
\def\safe#1{%
|
||||
\ifdefined#1%
|
||||
#1%
|
||||
\else%
|
||||
{\color{red}\bf?}%
|
||||
\fi%
|
||||
}
|
||||
|
||||
%% define a label for the latest tag
|
||||
%% label defines a command containing the string stored in \tag
|
||||
\def\deflabel{
|
||||
\def\label##1{\expandafter\outdef{label@##1}{\safe\tag}}
|
||||
|
||||
\def\ref##1{%
|
||||
% check whether the label is defined (hyperlink runs into errors if this check is omitted)
|
||||
\ifcsname label@##1@hl\endcsname%
|
||||
\hyperlink{ln.\csname label@##1@hl\endcsname}{{\color{blue}\safe\csname label@##1\endcsname}}%
|
||||
\else%
|
||||
\ifcsname label@##1\endcsname%
|
||||
{\color{blue}\csname ##1\endcsname}%
|
||||
\else%
|
||||
{\bf ??}%
|
||||
\fi%
|
||||
\fi%
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
%% make a custom link at any given location in the document
|
||||
\def\makelink#1#2{%
|
||||
\hrefanchor%
|
||||
\outdef{label@#1}{#2}%
|
||||
}
|
||||
|
||||
|
||||
%% section command
|
||||
% counter
|
||||
\newcounter{sectioncount}
|
||||
% space before section
|
||||
\newlength\secskip
|
||||
\setlength\secskip{40pt}
|
||||
% a prefix to put before the section number, e.g. A for appendices
|
||||
\def\sectionprefix{}
|
||||
% define some lengths
|
||||
\newlength\secnumwidth
|
||||
\newlength\sectitlewidth
|
||||
\def\section#1{
|
||||
% reset counters
|
||||
\stepcounter{sectioncount}
|
||||
\setcounter{subsectioncount}{0}
|
||||
\ifsectionsineq
|
||||
\setcounter{seqcount}0
|
||||
\fi
|
||||
\ifsectionsinfig
|
||||
\setcounter{figcount}0
|
||||
\fi
|
||||
|
||||
% space before section (if not first)
|
||||
\ifnum\thesectioncount>1
|
||||
\vskip\secskip
|
||||
\penalty-1000
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\Large\sectionprefix\thesectioncount.\hskip10pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\Large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@sec.\thesectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
%space
|
||||
\par\penalty10000
|
||||
\bigskip\penalty10000
|
||||
}
|
||||
|
||||
%% subsection
|
||||
% counter
|
||||
\newcounter{subsectioncount}
|
||||
% space before subsection
|
||||
\newlength\subsecskip
|
||||
\setlength\subsecskip{30pt}
|
||||
\def\subsection#1{
|
||||
% counters
|
||||
\stepcounter{subsectioncount}
|
||||
\setcounter{subsubsectioncount}{0}
|
||||
\ifsubsectionsineq
|
||||
\setcounter{seqcount}0
|
||||
\fi
|
||||
\ifsubsectionsinfig
|
||||
\setcounter{figcount}0
|
||||
\fi
|
||||
|
||||
% space before subsection (if not first)
|
||||
\ifnum\thesubsectioncount>1
|
||||
\vskip\subsecskip
|
||||
\penalty-500
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\large\hskip.5cm\sectionprefix\thesectioncount.\thesubsectioncount.\hskip5pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsec.\thesectioncount.\thesubsectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsubsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
% space
|
||||
\par\penalty10000
|
||||
\medskip\penalty10000
|
||||
}
|
||||
|
||||
%% subsubsection
|
||||
% counter
|
||||
\newcounter{subsubsectioncount}
|
||||
% space before subsubsection
|
||||
\newlength\subsubsecskip
|
||||
\setlength\subsubsecskip{20pt}
|
||||
\def\subsubsection#1{
|
||||
% counters
|
||||
\stepcounter{subsubsectioncount}
|
||||
|
||||
% space before subsubsection (if not first)
|
||||
\ifnum\thesubsubsectioncount>1
|
||||
\vskip\subsubsecskip
|
||||
\penalty-500
|
||||
\fi
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount}
|
||||
|
||||
% get widths
|
||||
\def\@secnum{{\bf\hskip1.cm\sectionprefix\thesectioncount.\thesubsectioncount.\thesubsubsectioncount.\hskip5pt}}
|
||||
\settowidth\secnumwidth{\@secnum}
|
||||
\setlength\sectitlewidth\textwidth
|
||||
\addtolength\sectitlewidth{-\secnumwidth}
|
||||
% print name
|
||||
\parbox{\textwidth}{
|
||||
\@secnum
|
||||
\parbox[t]{\sectitlewidth}{\large\bf #1}}
|
||||
|
||||
% write to table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsubsec.\thesectioncount.\thesubsectioncount.\thesubsubsectioncount\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocsubsubsection{#1}{\thepage}}
|
||||
\fi
|
||||
|
||||
% space
|
||||
\par\penalty10000
|
||||
\medskip\penalty10000
|
||||
}
|
||||
|
||||
%% itemize
|
||||
\newlength\itemizeskip
|
||||
% left margin for items
|
||||
\setlength\itemizeskip{20pt}
|
||||
\newlength\itemizeseparator
|
||||
% space between the item symbol and the text
|
||||
\setlength\itemizeseparator{5pt}
|
||||
% penalty preceding an itemize
|
||||
\newcount\itemizepenalty
|
||||
\itemizepenalty=0
|
||||
% counter counting the itemize level
|
||||
\newcounter{itemizecount}
|
||||
|
||||
% item symbol
|
||||
\def\itemizept#1{
|
||||
\ifnum#1=1
|
||||
\textbullet
|
||||
\else
|
||||
$\scriptstyle\blacktriangleright$
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
\newlength\current@itemizeskip
|
||||
\setlength\current@itemizeskip{0pt}
|
||||
\def\itemize{%
|
||||
\par\expandafter\penalty\the\itemizepenalty\medskip\expandafter\penalty\the\itemizepenalty%
|
||||
\addtocounter{itemizecount}{1}%
|
||||
\addtolength\current@itemizeskip{\itemizeskip}%
|
||||
\leftskip\current@itemizeskip%
|
||||
}
|
||||
\def\enditemize{%
|
||||
\addtocounter{itemizecount}{-1}%
|
||||
\addtolength\current@itemizeskip{-\itemizeskip}%
|
||||
\par\expandafter\penalty\the\itemizepenalty\leftskip\current@itemizeskip%
|
||||
\medskip\expandafter\penalty\the\itemizepenalty%
|
||||
}
|
||||
|
||||
% item, with optional argument to specify the item point
|
||||
% @itemarg is set to true when there is an optional argument
|
||||
\newif\if@itemarg
|
||||
\def\item{%
|
||||
% check whether there is an optional argument (if there is none, add on empty '[]')
|
||||
\@ifnextchar [{\@itemargtrue\@itemx}{\@itemargfalse\@itemx[]}%
|
||||
}
|
||||
\newlength\itempt@total
|
||||
\def\@itemx[#1]{
|
||||
\if@itemarg
|
||||
\settowidth\itempt@total{#1}
|
||||
\else
|
||||
\settowidth\itempt@total{\itemizept\theitemizecount}
|
||||
\fi
|
||||
\addtolength\itempt@total{\itemizeseparator}
|
||||
\par
|
||||
\medskip
|
||||
\if@itemarg
|
||||
\hskip-\itempt@total#1\hskip\itemizeseparator
|
||||
\else
|
||||
\hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
|
||||
\fi
|
||||
}
|
||||
|
||||
%% prevent page breaks after itemize
|
||||
\newcount\previtemizepenalty
|
||||
\def\nopagebreakafteritemize{
|
||||
\previtemizepenalty=\itemizepenalty
|
||||
\itemizepenalty=10000
|
||||
}
|
||||
%% back to previous value
|
||||
\def\restorepagebreakafteritemize{
|
||||
\itemizepenalty=\previtemizepenalty
|
||||
}
|
||||
|
||||
%% enumerate
|
||||
\newcounter{enumerate@count}
|
||||
\def\enumerate{
|
||||
\setcounter{enumerate@count}0
|
||||
\let\olditem\item
|
||||
\let\olditemizept\itemizept
|
||||
\def\item{
|
||||
% counter
|
||||
\stepcounter{enumerate@count}
|
||||
% set header
|
||||
\def\itemizept{\theenumerate@count.}
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\theenumerate@count}
|
||||
\olditem
|
||||
}
|
||||
\itemize
|
||||
}
|
||||
\def\endenumerate{
|
||||
\enditemize
|
||||
\let\item\olditem
|
||||
\let\itemizept\olditemizept
|
||||
}
|
||||
|
||||
|
||||
%% equation numbering
|
||||
% counter
|
||||
\newcounter{seqcount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\newif\ifsectionsineq
|
||||
\newif\ifsubsectionsineq
|
||||
\def\seqcount{
|
||||
\stepcounter{seqcount}
|
||||
% the output
|
||||
\edef\seqformat{\theseqcount}
|
||||
% add subsection number
|
||||
\ifsubsectionsineq
|
||||
\let\tmp\seqformat
|
||||
\edef\seqformat{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionsineq
|
||||
\let\tmp\seqformat
|
||||
\edef\seqformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\seqformat}
|
||||
% write number
|
||||
\marginnote{\hfill(\seqformat)}
|
||||
}
|
||||
%% equation environment compatibility
|
||||
\def\equation{\hrefanchor$$\seqcount}
|
||||
\def\endequation{$$\@ignoretrue}
|
||||
|
||||
|
||||
%% figures
|
||||
% counter
|
||||
\newcounter{figcount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\newif\ifsectionsinfig
|
||||
\newif\ifsubsectionsinfig
|
||||
% width of figures
|
||||
\newlength\figwidth
|
||||
\setlength\figwidth\textwidth
|
||||
\addtolength\figwidth{-2.5cm}
|
||||
% caption
|
||||
\def\defcaption{
|
||||
\long\def\caption##1{
|
||||
\stepcounter{figcount}
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
|
||||
% the number of the figure
|
||||
\edef\figformat{\thefigcount}
|
||||
% add subsection number
|
||||
\ifsubsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\figformat}
|
||||
|
||||
% write
|
||||
\hfil fig \figformat: \parbox[t]{\figwidth}{\leavevmode\small##1}
|
||||
|
||||
% space
|
||||
\par\bigskip
|
||||
}
|
||||
}
|
||||
%% short caption: centered
|
||||
\def\captionshort#1{
|
||||
\stepcounter{figcount}
|
||||
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
|
||||
% the number of the figure
|
||||
\edef\figformat{\thefigcount}
|
||||
% add section number
|
||||
\ifsectionsinfig
|
||||
\let\tmp\figformat
|
||||
\edef\figformat{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\figformat}
|
||||
|
||||
% write
|
||||
\hfil fig \figformat: {\small#1}
|
||||
|
||||
%space
|
||||
\par\bigskip
|
||||
}
|
||||
|
||||
%% environment
|
||||
\def\figure{
|
||||
\par
|
||||
\vfil\penalty100\vfilneg
|
||||
\bigskip
|
||||
}
|
||||
\def\endfigure{
|
||||
\par
|
||||
\bigskip
|
||||
}
|
||||
|
||||
|
||||
%% start appendices
|
||||
\def\appendix{
|
||||
\vfill
|
||||
\pagebreak
|
||||
|
||||
% counter
|
||||
\setcounter{sectioncount}0
|
||||
|
||||
% prefix
|
||||
\def\sectionprefix{A}
|
||||
|
||||
% write
|
||||
{\bf \LARGE Appendices}\par\penalty10000\bigskip\penalty10000
|
||||
|
||||
% add a mention in the table of contents
|
||||
\iftoc
|
||||
\immediate\write\tocoutput{\noexpand\tocappendices}\penalty10000
|
||||
\fi
|
||||
|
||||
%% uncomment for new page for each appendix
|
||||
%\def\seqskip{\vfill\pagebreak}
|
||||
}
|
||||
|
||||
|
||||
%% bibliography
|
||||
% size of header
|
||||
\newlength\bibheader
|
||||
\def\thebibliography#1{
|
||||
\hrefanchor
|
||||
|
||||
% add a mention in the table of contents
|
||||
\iftoc
|
||||
% save lncount in aux variable which is written to toc
|
||||
\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@references\endcsname{\thelncount}}
|
||||
\write\tocoutput{\noexpand\tocreferences{\thepage}}\penalty10000
|
||||
\fi
|
||||
|
||||
% write
|
||||
{\bf \LARGE References}\par\penalty10000\bigskip\penalty10000
|
||||
% width of header
|
||||
\settowidth\bibheader{[#1]}
|
||||
\leftskip\bibheader
|
||||
}
|
||||
% end environment
|
||||
\def\endthebibliography{
|
||||
\par\leftskip0pt
|
||||
}
|
||||
|
||||
%% bibitem command
|
||||
\def\bibitem[#1]#2{%
|
||||
\hrefanchor%
|
||||
\outdef{label@cite#2}{#1}%
|
||||
\hskip-\bibheader%
|
||||
\makebox[\bibheader]{\cite{#2}\hfill}%
|
||||
}
|
||||
|
||||
%% cite command (adapted from latex.ltx)
|
||||
% @tempswa is set to true when there is an optional argument
|
||||
\newif\@tempswa
|
||||
\def\cite{%
|
||||
% check whether there is an optional argument (if there is none, add on empty '[]')
|
||||
\@ifnextchar [{\@tempswatrue\@citex}{\@tempswafalse\@citex[]}%
|
||||
}
|
||||
% command with optional argument
|
||||
\def\@citex[#1]#2{\leavevmode%
|
||||
% initialize loop
|
||||
\let\@citea\@empty%
|
||||
% format
|
||||
\@cite{%
|
||||
% loop over ',' separated list
|
||||
\@for\@citeb:=#2\do{%
|
||||
% text to add at each iteration of the loop (separator between citations)
|
||||
\@citea\def\@citea{,\ }%
|
||||
% add entry to citelist
|
||||
\@writecitation{\@citeb}%
|
||||
\ref{cite\@citeb}%
|
||||
}%
|
||||
}%
|
||||
% add optional argument text (as an argument to '\@cite')
|
||||
{#1}%
|
||||
}
|
||||
\def\@cite#1#2{%
|
||||
[#1\if@tempswa , #2\fi]%
|
||||
}
|
||||
%% add entry to citelist after checking it has not already been added
|
||||
\def\@writecitation#1{%
|
||||
\ifcsname if#1cited\endcsname%
|
||||
\else%
|
||||
\expandafter\newif\csname if#1cited\endcsname%
|
||||
\immediate\write\@auxout{\string\citation{#1}}%
|
||||
\fi%
|
||||
}
|
||||
|
||||
%% table of contents
|
||||
% boolean
|
||||
\newif\iftoc
|
||||
\def\tableofcontents{
|
||||
{\bf \large Table of contents:}\par\penalty10000\bigskip\penalty10000
|
||||
|
||||
% copy content from file
|
||||
\IfFileExists{\jobname.toc}{\input{\jobname.toc}}{{\tt error: table of contents missing}}
|
||||
|
||||
% open new toc
|
||||
\newwrite\tocoutput
|
||||
\immediate\openout\tocoutput=\jobname.toc
|
||||
|
||||
\toctrue
|
||||
}
|
||||
%% close file
|
||||
\AtEndDocument{
|
||||
% close toc
|
||||
\iftoc
|
||||
\immediate\closeout\tocoutput
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% fill line with dots
|
||||
\def\leaderfill{\leaders\hbox to 1em {\hss. \hss}\hfill}
|
||||
|
||||
%% same as sectionprefix
|
||||
\def\tocsectionprefix{}
|
||||
|
||||
%% toc formats
|
||||
\newcounter{tocsectioncount}
|
||||
\def\tocsection #1#2{
|
||||
\stepcounter{tocsectioncount}
|
||||
\setcounter{tocsubsectioncount}{0}
|
||||
\setcounter{tocsubsubsectioncount}{0}
|
||||
% write
|
||||
\smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt {\color{blue}#1}\leaderfill#2}\par
|
||||
}
|
||||
\newcounter{tocsubsectioncount}
|
||||
\def\tocsubsection #1#2{
|
||||
\stepcounter{tocsubsectioncount}
|
||||
\setcounter{tocsubsubsectioncount}{0}
|
||||
% write
|
||||
{\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
||||
}
|
||||
\newcounter{tocsubsubsectioncount}
|
||||
\def\tocsubsubsection #1#2{
|
||||
\stepcounter{tocsubsubsectioncount}
|
||||
% write
|
||||
{\hskip20pt\hyperlink{ln.\csname toc@subsubsec.\thetocsectioncount.\thetocsubsectioncount.\thetocsubsubsectioncount\endcsname}{{\bf \thetocsubsubsectioncount}.\hskip5pt {\color{blue}\small #1}\leaderfill#2}}\par
|
||||
}
|
||||
\def\tocappendices{
|
||||
\medskip
|
||||
\setcounter{tocsectioncount}0
|
||||
{\bf Appendices}\par
|
||||
\smallskip
|
||||
\def\tocsectionprefix{A}
|
||||
}
|
||||
\def\tocreferences#1{
|
||||
\medskip
|
||||
{\hyperlink{ln.\csname toc@references\endcsname}{{\color{blue}\bf References}\leaderfill#1}}\par
|
||||
\smallskip
|
||||
}
|
||||
|
||||
|
||||
%% definitions that must be loaded at begin document
|
||||
\let\ian@olddocument\document
|
||||
\def\document{
|
||||
\ian@olddocument
|
||||
|
||||
\deflabel
|
||||
\defcaption
|
||||
}
|
||||
|
||||
%% end
|
||||
\ian@defaultoptions
|
||||
\endinput
|
||||
162
libs/iantheo.sty
Normal file
162
libs/iantheo.sty
Normal file
@ -0,0 +1,162 @@
|
||||
%%
|
||||
%% iantheorem package:
|
||||
%% Ian's customized theorem command
|
||||
%%
|
||||
|
||||
%% boolean to signal that this package was loaded
|
||||
\newif\ifiantheo
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% package name
|
||||
\ProvidesPackage{iantheo}[2016/11/10]
|
||||
|
||||
%% options
|
||||
\newif\ifsectionintheo
|
||||
\DeclareOption{section_in_theo}{\sectionintheotrue}
|
||||
\DeclareOption{no_section_in_theo}{\sectionintheofalse}
|
||||
\newif\ifsubsectionintheo
|
||||
\DeclareOption{subsection_in_theo}{\subsectionintheotrue}
|
||||
\DeclareOption{no_subsection_in_theo}{\subsectionintheofalse}
|
||||
|
||||
\def\iantheo@defaultoptions{
|
||||
\ExecuteOptions{section_in_theo, no_subsection_in_theo}
|
||||
\ProcessOptions
|
||||
|
||||
%%% reset at every new section
|
||||
\ifsectionintheo
|
||||
\let\iantheo@oldsection\section
|
||||
\gdef\section{\setcounter{theocount}{0}\iantheo@oldsection}
|
||||
\fi
|
||||
|
||||
%% reset at every new subsection
|
||||
\ifsubsectionintheo
|
||||
\let\iantheo@oldsubsection\subsection
|
||||
\gdef\subsection{\setcounter{theocount}{0}\iantheo@oldsubsection}
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% delimiters
|
||||
\def\delimtitle#1{
|
||||
\par%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\ \lower.3em\hbox{#1}\ %
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% callable by ref
|
||||
\def\delimtitleref#1{
|
||||
\par%
|
||||
%
|
||||
\ifdefined\ianclass%
|
||||
% hyperref anchor%
|
||||
\hrefanchor%
|
||||
% define tag (for \label)%
|
||||
\xdef\tag{#1}%
|
||||
\fi%
|
||||
%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\ \lower.3em\hbox{\bf #1}\ %
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% no title
|
||||
\def\delim{
|
||||
\par%
|
||||
\leavevmode\raise.3em\hbox to\hsize{%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
\hrulefill%
|
||||
\lower0.3em\hbox{\vrule height0.3em}%
|
||||
}%
|
||||
\par\penalty10000%
|
||||
}
|
||||
|
||||
%% end delim
|
||||
\def\enddelim{
|
||||
\par\penalty10000%
|
||||
\leavevmode%
|
||||
\raise.3em\hbox to\hsize{%
|
||||
\vrule height0.3em\hrulefill\vrule height0.3em%
|
||||
}%
|
||||
\par%
|
||||
}
|
||||
|
||||
|
||||
%% theorem
|
||||
% counter
|
||||
\newcounter{theocount}
|
||||
% booleans (write section or subsection in equation number)
|
||||
\def\theo#1{
|
||||
\stepcounter{theocount}
|
||||
\ifdefined\ianclass
|
||||
% hyperref anchor
|
||||
\hrefanchor
|
||||
\fi
|
||||
% the number
|
||||
\def\formattheo{\thetheocount}
|
||||
% add subsection number
|
||||
\ifsubsectionintheo
|
||||
\let\tmp\formattheo
|
||||
\edef\formattheo{\thesubsectioncount.\tmp}
|
||||
\fi
|
||||
% add section number
|
||||
\ifsectionintheo
|
||||
\let\tmp\formattheo
|
||||
\edef\formattheo{\sectionprefix\thesectioncount.\tmp}
|
||||
\fi
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\formattheo}
|
||||
% write
|
||||
\delimtitle{\bf #1 \formattheo}
|
||||
}
|
||||
\let\endtheo\enddelim
|
||||
%% theorem headers with name
|
||||
\def\theoname#1#2{
|
||||
\theo{#1}\hfil({\it #2})\par\penalty10000\medskip%
|
||||
}
|
||||
|
||||
|
||||
%% qed symbol
|
||||
\def\qedsymbol{$\square$}
|
||||
\def\qed{\penalty10000\hfill\penalty10000\qedsymbol}
|
||||
|
||||
|
||||
%% compatibility with article class
|
||||
\ifdefined\ianclasstrue
|
||||
\relax
|
||||
\else
|
||||
\def\thesectioncount{\thesection}
|
||||
\def\thesubsectioncount{\thesubsection}
|
||||
\def\sectionprefix{}
|
||||
\fi
|
||||
|
||||
|
||||
%% prevent page breaks after displayed equations
|
||||
\newcount\prevpostdisplaypenalty
|
||||
\def\nopagebreakaftereq{
|
||||
\prevpostdisplaypenalty=\postdisplaypenalty
|
||||
\postdisplaypenalty=10000
|
||||
}
|
||||
%% back to previous value
|
||||
\def\restorepagebreakaftereq{
|
||||
\postdisplaypenalty=\prevpostdisplaypenalty
|
||||
}
|
||||
|
||||
|
||||
%% end
|
||||
\iantheo@defaultoptions
|
||||
\endinput
|
||||
106
libs/point.sty
Normal file
106
libs/point.sty
Normal file
@ -0,0 +1,106 @@
|
||||
%%
|
||||
%% Points package:
|
||||
%% \point commands
|
||||
%%
|
||||
|
||||
%% TeX format
|
||||
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
|
||||
|
||||
%% package name
|
||||
\ProvidesPackage{point}[2017/06/13]
|
||||
|
||||
%% options
|
||||
\newif\ifresetatsection
|
||||
\DeclareOption{reset_at_section}{\resetatsectiontrue}
|
||||
\DeclareOption{no_reset_at_section}{\resetatsectionfalse}
|
||||
\newif\ifresetatsubsection
|
||||
\DeclareOption{reset_at_subsection}{\resetatsubsectiontrue}
|
||||
\DeclareOption{no_reset_at_subsection}{\resetatsubsectionfalse}
|
||||
\newif\ifresetattheo
|
||||
\DeclareOption{reset_at_theo}{\resetattheotrue}
|
||||
\DeclareOption{no_reset_at_theo}{\resetattheofalse}
|
||||
|
||||
\def\point@defaultoptions{
|
||||
\ExecuteOptions{reset_at_section, reset_at_subsection, no_reset_at_theo}
|
||||
\ProcessOptions
|
||||
|
||||
%% reset at every new section
|
||||
\ifresetatsection
|
||||
\let\point@oldsection\section
|
||||
\gdef\section{\resetpointcounter\point@oldsection}
|
||||
\fi
|
||||
%% reset at every new subsection
|
||||
\ifresetatsubsection
|
||||
\let\point@oldsubsection\subsection
|
||||
\gdef\subsection{\resetpointcounter\point@oldsubsection}
|
||||
\fi
|
||||
|
||||
%% reset at every new theorem
|
||||
\ifresetattheo
|
||||
\ifdefined\iantheotrue
|
||||
\let\point@oldtheo\theo
|
||||
\gdef\theo{\resetpointcounter\point@oldtheo}
|
||||
\fi
|
||||
\fi
|
||||
}
|
||||
|
||||
|
||||
%% point
|
||||
% counter
|
||||
\newcounter{pointcount}
|
||||
\def\point{
|
||||
\stepcounter{pointcount}
|
||||
\setcounter{subpointcount}{0}
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount}
|
||||
\fi
|
||||
% header
|
||||
\indent{\bf \thepointcount\ - }
|
||||
}
|
||||
|
||||
%% subpoint
|
||||
% counter
|
||||
\newcounter{subpointcount}
|
||||
\def\subpoint{
|
||||
\stepcounter{subpointcount}
|
||||
\setcounter{subsubpointcount}0
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount-\thesubpointcount}
|
||||
\fi
|
||||
% header
|
||||
\indent\hskip.5cm{\bf \thepointcount-\thesubpointcount\ - }
|
||||
}
|
||||
|
||||
%% subsubpoint
|
||||
% counter
|
||||
\newcounter{subsubpointcount}
|
||||
\def\subsubpoint{
|
||||
\stepcounter{subsubpointcount}
|
||||
% hyperref anchor (only if the class is 'ian')
|
||||
\ifdefined\ifianclass
|
||||
\hrefanchor
|
||||
% define tag (for \label)
|
||||
\xdef\tag{\thepointcount-\thesubpointcount-\thesubsubpointcount}
|
||||
\fi
|
||||
\indent\hskip1cm{\bf \thepointcount-\thesubpointcount-\thesubsubpointcount\ - }
|
||||
}
|
||||
|
||||
|
||||
%% reset point counters
|
||||
\def\resetpointcounter{
|
||||
\setcounter{pointcount}{0}
|
||||
\setcounter{subpointcount}{0}
|
||||
\setcounter{subsubpointcount}{0}
|
||||
}
|
||||
|
||||
|
||||
|
||||
%% end
|
||||
\point@defaultoptions
|
||||
\endinput
|
||||
Loading…
Reference in New Issue
Block a user