articles/18ccjl
1
Fork 0
Code Packages Releases Activity

Initial commit

Browse Source
This commit is contained in:
Ian Jauslin
2018-10-12 20:24:46 +00:00
commit 0425ca5693
22 changed files with 2215 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

30
figs/contour.fig/Makefile Normal file
View File

@ -0,0 +1,30 @@
PROJECTNAME=contour
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): poles.tikz.tex
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
poles.tikz.tex:
python3 contour.py > poles.tikz.tex
install: $(PDFS)
cp $^ $(INSTALLDIR)/
$(LIBS):
ln -fs libs/$@ ./
clean-libs:
rm -f $(LIBS)
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
rm -f poles.tikz.tex
clean-tex:
rm -f $(PDFS)
clean: clean-libs clean-aux clean-tex

82
figs/contour.fig/contour.py Normal file
View File

@ -0,0 +1,82 @@
#!/usr/bin/env python3
import cmath
import math
import scipy.special as sp
from scipy import optimize as op
import random
import sys
# number of roots
nr_roots=4
# size of plot
plotsize_x=3
plotsize_y=3
# rescale plot (so roots are not too close together)
plotsize_scale_x=1
plotsize_scale_y=6
# numerical values
hbar=6.58e-16 # eV.s
m=9.11e-31 # kg
Vn=9 # eV
En=20e9 # V/m
V=1
E=En*hbar/(Vn**1.5*m**0.5)*math.sqrt(1.60e-19)
# sqrt with branch cut along iR_+
def sqrt_p(x):
r,p=cmath.polar(x)
if(p<cmath.pi/2):
return(cmath.rect(math.sqrt(r),p/2))
else:
return(cmath.rect(math.sqrt(r),(p-2*math.pi)/2))
# solution of (-\Delta+V-ip)phi=0
def phi(p,x,E,V):
return(sp.airy(cmath.exp(-1j*math.pi/3)*(E**(1/3)*x-E**(-2/3)*(V-1j*p)))[0])
# its derivative
def dphi(p,x,E,V):
return(cmath.exp(-1j*math.pi/3)*E**(1/3)*sp.airy(cmath.exp(-1j*math.pi/3)*(E**(1/3)*x-E**(-2/3)*(V-1j*p)))[1])
# the function whose roots are to be computed and its derivative
def f(p):
return(sqrt_p(-1j*p)*phi(p,0,E,V)-dphi(p,0,E,V))
def df(p):
return(-1j/(2*sqrt_p(-1j*p))*phi(p,0,E,V)+sqrt_p(-1j*p)*dp_phi(p,0,E,V)-dp_dphi(p,0,E,V))
# derivatives of phi with respect to p
def dp_phi(p,x,E,V):
return(1j*cmath.exp(-1j*math.pi/3)*E**(-2/3)*sp.airy(cmath.exp(-1j*math.pi/3)*(E**(1/3)*x-E**(-2/3)*(V-1j*p)))[1])
def dp_dphi(p,x,E,V):
return(-1j*(x-(V-1j*p)/E)*phi(p,x,E,V))
# check whether the root was already found
def check(root,roots):
# reject if the root doesn't fit on the plot
if(plotsize_scale_x*root.real<-plotsize_x or abs(plotsize_scale_y*root.imag)>plotsize_y):
return(False)
for x in roots:
if(abs(root-x)<1e-12):
return(False)
return(True)
# find roots
roots=[]
while len(roots)<nr_roots:
try:
root=op.newton(f, -random.random()*plotsize_x/plotsize_scale_x+(2*random.random()-1)*plotsize_y/plotsize_scale_y*1j, fprime=df)
if(check(root,roots)):
roots.append(root)
print("found "+str(len(roots))+" roots of "+str(nr_roots), file=sys.stderr)
except RuntimeError:
root=0
except:
break
# print result
for root in roots:
print("\\pole{(% .3f,% .3f)}" % (plotsize_scale_x*root.real,plotsize_scale_y*root.imag))

34
figs/contour.fig/contour.tikz.tex Normal file
View File

@ -0,0 +1,34 @@
\documentclass{standalone}
\usepackage{tikz}
\def\pole#1{
\draw#1++(0.1,0.1)--++(-0.2,-0.2);
\draw#1++(-0.1,0.1)--++(0.2,-0.2);
\draw[color=red, line width=1pt]#1circle(0.3);
}
\begin{document}
\begin{tikzpicture}
% branch cut
\fill[color=gray](-3.3,-0.1)--++(3.3,0)--++(0,0.2)--++(-3.3,0)--cycle;
% axes
\draw(-3.3,0)--++(6.6,0);
\draw(0,-3.3)--++(0,6.6);
% -ik0^2
\pole{(0,-2)}
% other poles
\input{poles.tikz}
% contour
\draw[color=red, line width=1pt](-3.3,-0.3)--++(3.3,0);
\draw[color=red, line width=1pt](0,-0.3)..controls(0.3,-0.3)and(0.3,0.3)..(0,0.3);
\draw[color=red, line width=1pt](-3.3,0.3)--++(3.3,0);
\end{tikzpicture}
\end{document}

28
figs/libs/Makefile Normal file
View File

@ -0,0 +1,28 @@
PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
LIBS=$(notdir $(wildcard libs/*))
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(LIBS)
echo $(LIBS)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
install: $(PDFS)
cp $^ $(INSTALLDIR)/
$(LIBS):
ln -fs libs/$@ ./
clean-libs:
rm -f $(LIBS)
clean-aux:
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-tex:
rm -f $(PDFS)
clean: clean-libs clean-aux clean-tex

170
figs/plots.fig/FN_base.jl Normal file
View File

@ -0,0 +1,170 @@
# fractional power with an arbitrary branch cut
function pow(x,a,cut)
if(angle(x)/cut<=1)
return(abs(x)^a*exp(1im*angle(x)*a))
else
return(abs(x)^a*exp(1im*(angle(x)-sign(cut)*2*pi)*a))
end
end
# asymptotic airy functions
# specify a branch cut for the fractional power
function airyai_asym(x,cut)
if(abs(real(pow(x,3/2,cut)))<airy_threshold)
return(exp(2/3*pow(x,3/2,cut))*airyai(x))
else
ret=0
for n in 0:airy_order
ret+=gamma(n+5/6)*gamma(n+1/6)*(-3/4)^n/(4*pi^(3/2)*factorial(n)*pow(x,3*n/2+1/4,cut))
end
return ret
end
end
function airyaiprime_asym(x,cut)
if(abs(real(pow(x,3/2,cut)))<airy_threshold)
return(exp(2/3*pow(x,3/2,cut))*airyaiprime(x))
else
ret=0
for n in 0:airy_order
ret+=gamma(n+5/6)*gamma(n+1/6)*(-3/4)^n/(4*pi^(3/2)*factorial(n))*(-1/pow(x,3*n/2-1/4,cut)-(3/2*n+1/4)/pow(x,3*n/2+5/4,cut))
end
return ret
end
end
# solutions of (-\Delta+U-ip)phi=0
# assume that p has an infinitesimal real part (and adjust the branch cuts appropriately)
function phi(p,x,E,U)
return(airyai_asym(2^(1/3)*exp(-1im*pi/3)*(E^(1/3)*x-E^(-2/3)*(U-1im*p)),pi))
end
function dphi(p,x,E,U)
return(2^(1/3)*exp(-1im*pi/3)*E^(1/3)*airyaiprime_asym(2^(1/3)*exp(-1im*pi/3)*(E^(1/3)*x-E^(-2/3)*(U-1im*p)),pi))
end
function eta(p,x,E,U)
return(exp(-1im*pi/3)*airyai_asym(-2^(1/3)*(E^(1/3)*x-E^(-2/3)*(U-1im*p)),pi/2))
end
function deta(p,x,E,U)
return(-2^(1/3)*exp(-1im*pi/3)*E^(1/3)*airyaiprime_asym(-2^(1/3)*(E^(1/3)*x-E^(-2/3)*(U-1im*p)),pi/2))
end
# Laplace transform of psi
# assume that p has an infinitesimal real part (and adjust the branch cuts appropriately)
# for example, (1im*p-U)^(3/2) becomes pow(1im*p-U,3/2,-pi/2) because when 1im*p is real negative, its square root should be imaginary positive
function f(p,x,k0,E,U)
T=2im*k0/(1im*k0-sqrt(2*U-k0*k0))
R=T-1
if x>=0
C2=-2im*T/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))*((sqrt(2*U-k0*k0)+pow(-2im*p,1/2,pi/2))/(-2im*p+k0*k0)-2im*(2*E)^(-1/3)*pi*quadgk(y -> (pow(-2im*p,1/2,pi/2)*eta(p,0,E,U)-deta(p,0,E,U))*phi(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2))),0,Inf)[1])
FT=4*(2*E)^(-1/3)*pi*(quadgk(y -> phi(p,x,E,U)*eta(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2)-pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2))),0,x)[1]+quadgk(y -> eta(p,x,E,U)*phi(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2))),x,Inf)[1])
main=C2*phi(p,x,E,U)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2)))+T*FT
# subtract the contribution of the pole, which will be added back in after the integration
pole=psi_pole(x,k0,E,U)/(p+1im*k0*k0/2)
return(main-pole)
else
C1=-2im*T*((sqrt(2*U-k0*k0)*phi(p,0,E,U)+dphi(p,0,E,U))/(-2im*p+k0*k0)/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))+quadgk(y -> phi(p,y,E,U)/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2))),0,Inf)[1])
FI=-2im*exp(1im*k0*x)/(-2im*p+k0*k0)
FR=-2im*exp(-1im*k0*x)/(-2im*p+k0*k0)
main=C1*exp(pow(-2im*p,1/2,pi/2)*x)+FI+R*FR
# subtract the contribution of the pole, which will be added back in after the integration
pole=psi_pole(x,k0,E,U)/(p+1im*k0*k0/2)
return(main-pole)
end
end
# its derivative
function df(p,x,k0,E,U)
T=2im*k0/(1im*k0-sqrt(2*U-k0*k0))
R=T-1
if x>=0
C2=-2im*T/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))*((sqrt(2*U-k0*k0)+pow(-2im*p,1/2,pi/2))/(-2im*p+k0*k0)-2im*(2*E)^(-1/3)*pi*quadgk(y -> (pow(-2im*p,1/2,pi/2)*eta(p,0,E,U)-deta(p,0,E,U))*phi(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2))),0,Inf)[1])
dFT=4*(2*E)^(-1/3)*pi*(quadgk(y -> dphi(p,x,E,U)*eta(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2)-pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2))),0,x)[1]+quadgk(y -> deta(p,x,E,U)*phi(p,y,E,U)*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2))),x,Inf)[1])
main=C2*dphi(p,x,E,U)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2)))+T*dFT
# subtract the contribution of the pole, which will be added back in after the integration
pole=dpsi_pole(x,k0,E,U)/(p+1im*k0*k0/2)
return(main-pole)
else
C1=-2im*T*((sqrt(2*U-k0*k0)*phi(p,0,E,U)+dphi(p,0,E,U))/(-2im*p+k0*k0)/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))+quadgk(y -> phi(p,y,E,U)/(pow(-2im*p,1/2,pi/2)*phi(p,0,E,U)-dphi(p,0,E,U))*exp(-sqrt(2*U-k0*k0)*y)*exp(sqrt(2)*2im/3*(pow(E^(1/3)*y+E^(-2/3)*(1im*p-U),3/2,-pi/2)-E^(-1)*pow(1im*p-U,3/2,-pi/2))),0,Inf)[1])
dFI=2*k0*exp(1im*k0*x)/(-2im*p+k0*k0)
dFR=-2*k0*exp(-1im*k0*x)/(-2im*p+k0*k0)
main=C1*pow(-2im*p,1/2,pi/2)*exp(pow(-2im*p,1/2,pi/2)*x)+dFI+R*dFR
# subtract the contribution of the pole, which will be added back in after the integration
pole=dpsi_pole(x,k0,E,U)/(p+1im*k0*k0/2)
return(main-pole)
end
end
# psi (returns t,psi(x,t))
function psi(x,k0,E,U,p_npoints,p_cutoff)
fft=fourier_fft(f,x,k0,E,U,p_npoints,p_cutoff)
# add the contribution of the pole
for i in 1:p_npoints
fft[2][i]=fft[2][i]+psi_pole(x,k0,E,U)*exp(-1im*k0*k0/2*fft[1][i])
end
return(fft)
end
# its derivative
function dpsi(x,k0,E,U,p_npoints,p_cutoff)
fft=fourier_fft(df,x,k0,E,U,p_npoints,p_cutoff)
# add the contribution of the pole
for i in 1:p_npoints
fft[2][i]=fft[2][i]+dpsi_pole(x,k0,E,U)*exp(-1im*k0*k0/2*fft[1][i])
end
return(fft)
end
# compute Fourier transform by sampling and fft
function fourier_fft(A,x,k0,E,U,p_npoints,p_cutoff)
fun=zeros(Complex{Float64},p_npoints)
times=zeros(p_npoints)
# prepare fft
for i in 1:p_npoints
fun[i]=p_cutoff/pi*A(1im*(-p_cutoff+2*p_cutoff*(i-1)/p_npoints),x,k0,E,U)
times[i]=(i-1)*pi/p_cutoff
end
ifft!(fun)
# correct the phase
for i in 2:2:p_npoints
fun[i]=-fun[i]
end
return([times,fun])
end
# asymptotic value of psi
function psi_pole(x,k0,E,U)
if x>=0
return(1im*phi(-1im*k0*k0/2,x,E,U)*2*k0/(1im*k0*phi(-1im*k0*k0/2,0,E,U)+dphi(-1im*k0*k0/2,0,E,U))*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(k0*k0/2-U),3/2,-pi/2)-E^(-1)*pow(k0*k0/2-U,3/2,-pi/2))))
else
return((1im*k0*phi(-1im*k0*k0/2,0,E,U)-dphi(-1im*k0*k0/2,0,E,U))/(1im*k0*phi(-1im*k0*k0/2,0,E,U)+dphi(-1im*k0*k0/2,0,E,U))*exp(-1im*k0*x)+exp(1im*k0*x))
end
end
function dpsi_pole(x,k0,E,U)
if x>=0
return(1im*dphi(-1im*k0*k0/2,x,E,U)*2*k0/(1im*k0*phi(-1im*k0*k0/2,0,E,U)+dphi(-1im*k0*k0/2,0,E,U))*exp(sqrt(2)*2im/3*(pow(E^(1/3)*x+E^(-2/3)*(k0*k0/2-U),3/2,-pi/2)-E^(-1)*pow(k0*k0/2-U,3/2,-pi/2))))
else
return(-1im*k0*(1im*k0*phi(-1im*k0*k0/2,0,E,U)-dphi(-1im*k0*k0/2,0,E,U))/(1im*k0*phi(-1im*k0*k0/2,0,E,U)+dphi(-1im*k0*k0/2,0,E,U))*exp(-1im*k0*x)+1im*k0*exp(1im*k0*x))
end
end
# current
function J(ps,dps)
return(2*imag(conj(ps)*dps))
end
# complete computation of the current
function current(x,k0,E,U,p_npoints,p_cutoff)
ps=psi(x,k0,E,U,p_npoints,p_cutoff)
dps=dpsi(x,k0,E,U,p_npoints,p_cutoff)
Js=zeros(Complex{Float64},p_npoints)
for i in 1:p_npoints
Js[i]=J(ps[2][i],dps[2][i])
end
return(Js)
end

36
figs/plots.fig/Makefile Normal file
View File

@ -0,0 +1,36 @@
PROJECTNAME=currents-4 currents-8 density-4 density-8 integrated_current-4 integrated_current-8
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
currents-4.pdf density-4.pdf integrated_current-4.pdf: current_density-4.dat
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
currents-8.pdf density-8.pdf integrated_current-8.pdf: current_density-8.dat
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
current_density-4.dat:
julia current_density.jl 4 > $@
current_density-8.dat:
julia current_density.jl 8 > $@
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 current_density-4.dat
rm -f current_density-8.dat
clean-tex:
rm -f $(PDFS)
clean: clean-dat clean-aux clean-tex

60
figs/plots.fig/current_density.jl Normal file
View File

@ -0,0 +1,60 @@
using QuadGK
using FastGaussQuadrature
using SpecialFunctions
using FFTW
# numerical values
hbar=6.58e-16 # eV.s
m=9.11e-31 # kg
Un=9 # eV
En=parse(Float64,ARGS[1])*1e9 # V/m
Kn=4.5 # eV
# dimensionless quantities
U=1
E=En*hbar/(Un^1.5*m^0.5)*sqrt(1.60e-19)
k0=sqrt(2*Kn/Un)
# cutoffs
p_cutoff=20*k0
p_npoints=4096
# airy approximations
airy_threshold=30
airy_order=5
# order for Gauss-Legendre quadrature
order=10
# compute at these points
X=[(2*U-k0*k0)/(2*E),10*(2*U-k0*k0)/(2*E)]
include("FN_base.jl")
# compute the weights and abcissa for gauss-legendre quadratures
gl_data=gausslegendre(order)
ps=Array{Array{Array{Complex{Float64}}}}(undef,length(X))
dps=Array{Array{Array{Complex{Float64}}}}(undef,length(X))
intJ=Array{Array{Complex{Float64}}}(undef,length(X))
for i in 1:length(X)
# wave function
ps[i]=psi(X[i],k0,E,U,p_npoints,p_cutoff)
dps[i]=dpsi(X[i],k0,E,U,p_npoints,p_cutoff)
# integrated current
intJ[i]=zeros(Complex{Float64},p_npoints)
for l in 1:order
eval=current(X[i],k0/2*(gl_data[1][l]+1),E,U,p_npoints,p_cutoff)
for j in 1:length(eval)
intJ[i][j]=intJ[i][j]+k0/2*gl_data[2][l]*eval[j]
end
end
end
for j in 1:p_npoints
for i in 1:length(X)
print(real(ps[i][1][j])*hbar/Un*1e15,' ',abs(ps[i][2][j])^2,' ',J(ps[i][2][j],dps[i][2][j])/(2*k0),' ',real(intJ[i][j]/k0^2),' ')
end
print('\n')
end

43
figs/plots.fig/currents-4.gnuplot Normal file
View File

@ -0,0 +1,43 @@
## can also set the following options
set title "$E=4\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$\\displaystyle\\frac j{2k}$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot "current_density-4.dat" using 1:3 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-4.dat" using 5:7 every ::1 with lines linestyle 2 title "$x=10x_0$"

43
figs/plots.fig/currents-8.gnuplot Normal file
View File

@ -0,0 +1,43 @@
## can also set the following options
set title "$E=8\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$\\displaystyle\\frac j{2k}$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot "current_density-8.dat" using 1:3 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-8.dat" using 5:7 every ::1 with lines linestyle 2 title "$x=10x_0$"

44
figs/plots.fig/density-4.gnuplot Normal file
View File

@ -0,0 +1,44 @@
## can also set the following options
set title "$E=4\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$|\\psi|^2$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot \
"current_density-4.dat" using 1:2 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-4.dat" using 5:6 every ::1 with lines linestyle 2 title "$x=10x_0$"

44
figs/plots.fig/density-8.gnuplot Normal file
View File

@ -0,0 +1,44 @@
## can also set the following options
set title "$E=8\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$|\\psi|^2$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot \
"current_density-8.dat" using 1:2 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-8.dat" using 5:6 every ::1 with lines linestyle 2 title "$x=10x_0$"

43
figs/plots.fig/integrated_current-4.gnuplot Normal file
View File

@ -0,0 +1,43 @@
## can also set the following options
set title "$E=4\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$\\displaystyle\\frac J{k^2}$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot "current_density-4.dat" using 1:4 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-4.dat" using 5:8 every ::1 with lines linestyle 2 title "$x=10x_0$"

43
figs/plots.fig/integrated_current-8.gnuplot Normal file
View File

@ -0,0 +1,43 @@
## can also set the following options
set title "$E=4\\ \\mathrm{V}\\cdot\\mathrm{nm}^{-1}$"
set ylabel "$\\displaystyle\\frac J{k^2}$" norotate
set xlabel "$t$ (fs)"
#
## start ticks at 0, then every x
#set xtics 0,x
#set ytics 0,x
## puts 4 minor tics between tics (5 intervals, i.e. every 0.01)
set mxtics 5
set mytics 5
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 12.5,8.75 standalone
set key spacing 1.5
# 3=1+2 draw bottom and left sides of the box
set border 3
# don't show tics on opposite sides
set xtics nomirror
set ytics nomirror
# My colors
## 4169E1 (pastel blue)
## DC143C (bright red)
## 32CD32 (bright green)
## 4B0082 (deep purple)
## DAA520 (ochre)
# 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
set xrange [:12]
plot "current_density-8.dat" using 1:4 every ::1 with lines linestyle 1 title "$x=x_0$",\
"current_density-8.dat" using 5:8 every ::1 with lines linestyle 2 title "$x=10x_0$"

1
figs/potential.fig/Makefile Symbolic link
View File

@ -0,0 +1 @@
../libs/Makefile

22
figs/potential.fig/potential.tikz.tex Normal file
View File

@ -0,0 +1,22 @@
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw(-3,0)--(3,0);
\draw(0,-1.5)--(0,3);
\draw[line width=1.5pt](-2.5,0)--(0,0)--(0,2.5)--(1.975,-1.25);
\draw(1.5,1.5)node{\small$U-Ex$};
\draw[line width=1pt, densely dotted](-2.5,1)--(0,1);
\draw(-2.8,1)node{\small$E_F$};
\draw(0,3.3)node{\small$V$};
\draw(3.3,0)node{\small$x$};
\end{tikzpicture}
\end{document}