Update to v0.1:
Added: Theorem on positivity of solutions. Added: Reference to [CJLL20] Added: Theorem on decay rate is now more general. Fixed: Clarified the discussion in point 2-2 of the proof of the theorem on decay. Removed: open problem about positivity of solutions. Fixed: Format of named theorems. Fixed: Minor formatting fixes. Fixed: In proof of decay: indenting error.
This commit is contained in:
parent
e6bf8349d7
commit
196f3d05a9
File diff suppressed because it is too large
Load Diff
19
Changelog
Normal file
19
Changelog
Normal file
@ -0,0 +1,19 @@
|
|||||||
|
v0.1:
|
||||||
|
|
||||||
|
* Added: Theorem on positivity of solutions.
|
||||||
|
|
||||||
|
* Added: Reference to [CJLL20]
|
||||||
|
|
||||||
|
* Added: Theorem on decay rate is now more general.
|
||||||
|
|
||||||
|
* Fixed: Clarified the discussion in point 2-2 of the proof of the theorem
|
||||||
|
on decay.
|
||||||
|
|
||||||
|
* Removed: open problem about positivity of solutions.
|
||||||
|
|
||||||
|
* Fixed: Format of named theorems.
|
||||||
|
|
||||||
|
* Fixed: Minor formatting fixes.
|
||||||
|
|
||||||
|
* Fixed: In proof of decay: indenting error.
|
||||||
|
|
@ -1,42 +0,0 @@
|
|||||||
\bibitem[Bo47]{Bo47}N. Bogolubov - {\it On the theory of superfluidity}, Journal of Physics (USSR), volume\-~11, number\-~1 , pages\-~23-32 (translated from the Russian Izv.Akad.Nauk Ser.Fiz, volume\-~11, pages\-~77-90), 1947.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[CHe]{CHe}E.\-~Carlen, M.\-~Holzmann, I.\-~Jauslin, E.H.\-~Lieb, in preparation.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[Dy57]{Dy57}F.J. Dyson - {\it Ground-State Energy of a Hard-Sphere Gas}, Physical Review, volume\-~106, issue\-~1, pages\-~20-26, 1957,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1103/PhysRev.106.20}{10.1103/PhysRev.106.20}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[FS19]{FS19}S.\-~Fournais, J.P.\-~Solovej - {\it The energy of dilute Bose gases}, 2019,\par\penalty10000
|
|
||||||
arxiv:{\tt\href{http://arxiv.org/abs/1904.06164}{1904.06164}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[Ga99]{Ga99}G. Gallavotti - {\it Statistical mechanics, a short treatise}, Springer, 1999.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[LHY57]{LHY57}T.D. Lee, K. Huang, C.N. Yang - {\it Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties}, Physical Review, volume\-~106, issue\-~6, pages\-~1135-1145, 1957,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1103/PhysRev.106.1135}{10.1103/PhysRev.106.1135}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[Le29]{Le29}W. Lenz - {\it Die Wellenfunktion und Geschwindigkeitsverteilung des entarteten Gases}, Zeitschrift f\"ur Physik, volume\-~56, issue\-~11-12, pages\-~778-789, 1929,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1007/BF01340138}{10.1007/BF01340138}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[Li63]{Li63}E.H. Lieb - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas}, Physical Review, volume\-~130, issue\-~6, pages\-~2518-2528, 1963,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1103/PhysRev.130.2518}{10.1103/PhysRev.130.2518}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[LL64]{LL64}E.H. Lieb, W. Liniger - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. III. Application to the One-Dimensional Model}, Physical Review, volume\-~134, issue\-~2A, pages A312-A315, 1964,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1103/PhysRev.134.A312}{10.1103/PhysRev.134.A312}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[LL01]{LL01}E.H. Lieb, M. Loss - {\it Analysis}, Second edition, Graduate studies in mathematics, Americal Mathematical Society, 2001.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[LY98]{LY98}E.H. Lieb, J. Yngvason - {\it Ground State Energy of the Low Density Bose Gas}, Physical Review Letters, volume\-~80, issue\-~12, pages\-~2504-2507, 1998,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1103/PhysRevLett.80.2504}{10.1103/PhysRevLett.80.2504}}, arxiv:{\tt\href{http://arxiv.org/abs/cond-mat/9712138}{cond-mat/9712138}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[LY01]{LY01}E.H. Lieb, J. Yngvason - {\it The Ground State Energy of a Dilute Two-Dimensional Bose Gas}, Journal of Statistical Physics, volume\-~103, issue\-~3-4, pages\-~509-526, 2001,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1023/A:1010337215241}{10.1023/A:1010337215241}}, arxiv:{\tt\href{http://arxiv.org/abs/math-ph/0002014}{math-ph/0002014}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[PT12]{PT12}E. Pulvirenti, D. Tsagkarogiannis - {\it Cluster Expansion in the Canonical Ensemble}, Communications in Mathematical Physics, volume\-~316, issue\-~2, pages\-~289-306, 2012,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1007/s00220-012-1576-y}{10.1007/s00220-012-1576-y}}, arxiv:{\tt\href{http://arxiv.org/abs/1105.1022}{1105.1022}}.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[RS75]{RS75b}M. Reed, B. Simon - {\it Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness}, second edition, Academic Press, New York, 1975.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[Ru99]{Ru99}D. Ruelle - {\it Statistical mechanics: rigorous results}, Imperial College Press, World Scientific, (first edition: Benjamin, 1969), 1999.\par\medskip
|
|
||||||
|
|
||||||
\bibitem[YY09]{YY09}H. Yau, J. Yin - {\it The Second Order Upper Bound for the Ground Energy of a Bose Gas}, Journal of Statistical Physics, volume\-~136, issue\-~3, pages\-~453-503, 2009,\par\penalty10000
|
|
||||||
doi:{\tt\href{http://dx.doi.org/10.1007/s10955-009-9792-3}{10.1007/s10955-009-9792-3}}, arxiv:{\tt\href{http://arxiv.org/abs/0903.5347}{0903.5347}}.\par\medskip
|
|
||||||
|
|
Loading…
Reference in New Issue
Block a user