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2023-07-25 02:33:32 +00:00
\bibitem[AEe95]{AEe95}M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell - {\it Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor}, Science, volume\-~269, issue\-~5221, pages\-~198-201, 1995,\par\penalty10000
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\bibitem[BCS21]{BCS21}G. Basti, S. Cenatiempo, B. Schlein - {\it A new second-order upper bound for the ground state energy of dilute Bose gases}, Forum of Mathematics, Sigma, volume\-~9, number e74, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1017/fms.2021.66}{10.1017/fms.2021.66}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2101.06222}{2101.06222}}.\par\medskip
\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[Bo24]{Bo24}S.N. Bose - {\it Plancks Gesetz und Lichtquantenhypothese}, Weitschrift f\"ur Physik, volume\-~26, issue\-~1, pages\-~178-181, 1924,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/BF01327326}{10.1007/BF01327326}}.\par\medskip
\bibitem[CHe21]{CHe21}E.A. Carlen, M. Holzmann, I. Jauslin, E.H. Lieb - {\it Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy}, Physical Review A, volume\-~103, issue\-~5, number\-~053309, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevA.103.053309}{10.1103/PhysRevA.103.053309}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2011.10869}{2011.10869}}.\par\medskip
\bibitem[CJL20]{CJL20}E.A. Carlen, I. Jauslin, E.H. Lieb - {\it Analysis of a simple equation for the ground state energy of the Bose gas}, Pure and Applied Analysis, volume\-~2, issue\-~3, pages\-~659-684, 2020,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.2140/paa.2020.2.659}{10.2140/paa.2020.2.659}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1912.04987}{1912.04987}}.\par\medskip
\bibitem[CJL21]{CJL21}E.A. Carlen, I. Jauslin, E.H. Lieb - {\it Analysis of a Simple Equation for the Ground State of the Bose Gas II: Monotonicity, Convexity, and Condensate Fraction}, SIAM Journal on Mathematical Analysis, volume\-~53, number\-~5, pages\-~5322-5360, 2021,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1137/20M1376820}{10.1137/20M1376820}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2010.13882}{2010.13882}}.\par\medskip
\bibitem[DMe95]{DMe95}K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle - {\it Bose-Einstein Condensation in a Gas of Sodium Atoms}, Physical Review Letters, volume\-~75, issue\-~22, pages\-~3969-3973, 1995,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.75.3969}{10.1103/PhysRevLett.75.3969}}.\par\medskip
\bibitem[Ei24]{Ei24}A. Einstein - {\it Quantentheorie des einatomigen idealen Gases}, Sitzungsberichte der Preussischen Akademie der Wissenschaften, volume\-~1, issue\-~3, 1924.\par\medskip
\bibitem[FS20]{FS20}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases}, Annals of Mathematics, volume\-~192, issue\-~3, pages\-~893-976, 2020,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4007/annals.2020.192.3.5}{10.4007/annals.2020.192.3.5}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1904.06164}{1904.06164}}.\par\medskip
\bibitem[FS23]{FS23}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases II: the general case}, Inventiones mathematicae, volume\-~232, issue\-~2, pages\-~863-994, 2023,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00222-022-01175-0}{10.1007/s00222-022-01175-0}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2108.12022}{2108.12022}}.\par\medskip
\bibitem[Ga99]{Ga99}G. Gallavotti - {\it Statistical mechanics, a short treatise}, Springer, 1999.\par\medskip
\bibitem[Ja22]{Ja22}I. Jauslin - {\it Review of a Simplified Approach to study the Bose gas at all densities}, The Physics and Mathematics of Elliott Lieb, The\-~90th Anniversary Volume I, chapter\-~25, pages\-~609-635, ed. Rupert L. Frank, Ari Laptev, Mathieu Lewin, Robert Seiringer, EMS Press, 2022,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-1/25}{10.4171/90-1/25}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2202.07637}{2202.07637}}.\par\medskip
\bibitem[Ja23]{Ja23b}I.\-~Jauslin - {\it Evidence of a liquid phase in interacting Bosons at intermediate densities}, 2023,\par\penalty10000
arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2302.13449}{2302.13449}}.\par\medskip
\bibitem[Ja23b]{Ja23}I.\-~Jauslin - {\it The Simplified approach to the Bose gas without translation invariance}, 2023,\par\penalty10000
arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2302.13446}{2302.13446}}.\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\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.106.1135}{10.1103/PhysRev.106.1135}}.\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\color{blue}\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\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.134.A312}{10.1103/PhysRev.134.A312}}.\par\medskip
Update to v0.1: Fixed: H_N is not compact, e^{-H_N} is. Fixed: Removed confusing discussion of Anyons Added: Discussion of compactness.
2023-07-26 04:33:57 +00:00
\bibitem[LL01]{LL01}E.H. Lieb, M. Loss - {\it Analysis}, Second edition, Graduate studies in mathematics, Americal Mathematical Society, 2001.\par\medskip
Initial commit
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\bibitem[LS64]{LS64}E.H. Lieb, A.Y. Sakakura - {\it Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas. II. Charged Bose Gas at High Density}, Physical Review, volume\-~133, issue\-~4A, pages A899-A906, 1964,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.133.A899}{10.1103/PhysRev.133.A899}}.\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\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.80.2504}{10.1103/PhysRevLett.80.2504}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/cond-mat/9712138}{cond-mat/9712138}}.\par\medskip
\bibitem[Op31]{Op31}J.R. Oppenheimer - {\it Note on Light Quanta and the Electromagnetic Field}, Physical Review, volume\-~38, issue\-~4, pages\-~725-746, 1931,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.38.725}{10.1103/PhysRev.38.725}}.\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[Sc22]{Sc22}B. Schlein - {\it Bose gases in the Gross-Pitaevskii limit: A survey of some rigorous results}, The Physics and Mathematics of Elliott Lieb, The\-~90th anniversary volume II, eds R.L. Frank, A. Laptev, M. Lewin, R. Seiringer, pages\-~277-305, 2022,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-2/40}{10.4171/90-2/40}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2203.10855}{2203.10855}}.\par\medskip
\bibitem[Se11]{Se11}R. Seiringer - {\it The Excitation Spectrum for Weakly Interacting Bosons}, Communications in Mathematical Physics, volume\-~306, issue\-~2, pages\-~565-578, 2011,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-011-1261-6}{10.1007/s00220-011-1261-6}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1008.5349}{1008.5349}}.\par\medskip
Update to v0.1: Fixed: H_N is not compact, e^{-H_N} is. Fixed: Removed confusing discussion of Anyons Added: Discussion of compactness.
2023-07-26 04:33:57 +00:00
\bibitem[Te14]{Te14}G. Teschl - {\it Mathematical Methods in Quantum Mechanics With Applications to Schr\"odinger Operators}, Second Edition, Graduate Studies in Mathematics, volume\-~157, AMS, 2014.\par\medskip
Initial commit
2023-07-25 02:33:32 +00:00
\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\color{blue}\href{http://dx.doi.org/10.1007/s10955-009-9792-3}{10.1007/s10955-009-9792-3}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/0903.5347}{0903.5347}}.\par\medskip
\bibitem[JaSS]{ss}I.\-~Jauslin - {\tt simplesolv} software package v0.4.1,\par\penalty10000
{\tt\color{blue}\href{http://ian.jauslin.org/software/simplesolv}{http://ian.jauslin.org/software/simplesolv}}.\par\medskip
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