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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
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\bibitem[BBe18]{BBe18}C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein - {\it Complete Bose–Einstein Condensation in the Gross–Pitaevskii Regime}, Communications in Mathematical Physics, volume\-~359, issue\-~3, pages\-~975-1026, 2018,\par\penalty10000
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\bibitem[BBe19]{BBe19}C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein - {\it Bogoliubov theory in the Gross–Pitaevskii limit}, Acta Mathematica, volume\-~222, issue\-~2, pages\-~219-335, 2019,\par\penalty10000
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\bibitem[BBe20]{BBe20}C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein - {\it Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime}, Communications in Mathematical Physics, volume\-~376, issue\-~2, pages\-~1311-1395, 2020,\par\penalty10000
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\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[BSS22]{BSS22}C. Brennecke, B. Schlein, S. Schraven - {\it Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime}, Mathematical Physics, Analysis and Geometry, volume\-~25, issue\-~2, pages\-~1-71, 2022,\par\penalty10000
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\bibitem[BSS22b]{BSS22b}C. Brennecke, B. Schlein, S. Schraven - {\it Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime}, Annales Henri Poincaré, volume\-~23, issue\-~5, pages\-~1583-1658, 2022,\par\penalty10000
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\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
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\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
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\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
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\bibitem[DS20]{DS20}A. Deuchert, R. Seiringer - {\it Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature}, Archive for Rational Mechanics and Analysis, volume\-~236, issue\-~3, pages\-~1217-1271, 2020,\par\penalty10000
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\bibitem[DSY19]{DSY19}A. Deuchert, R. Seiringer, J. Yngvason - {\it Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature}, Communications in Mathematical Physics, volume\-~368, issue\-~2, pages\-~723-776, 2019,\par\penalty10000
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\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
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\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
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\bibitem[FS22]{FS22}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases II: the general case}, Inventiones mathematicae, volume , issue , pages\-~1-132, 2022,\par\penalty10000
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\bibitem[Gr61]{Gr61}E.P. Gross - {\it Structure of a quantized vortex in boson systems}, Il Nuovo Cimento (1955-1965), volume\-~20, issue\-~3, pages\-~454-477, 1961,\par\penalty10000
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\bibitem[HST22]{HST22}C.\-~Hainzl, B.\-~Schlein, A.\-~Triay - {\it Bogoliubov theory in the Gross-Pitaevskii limit}, arXiv preprint, 2022\par\penalty10000
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\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
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\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
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\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
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\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
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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
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\bibitem[LS02]{LS02}E.H. Lieb, R. Seiringer - {\it Proof of Bose-Einstein Condensation for Dilute Trapped Gases}, Physical Review Letters, volume\-~88, issue\-~17, number\-~170409, 2002,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRevLett.88.170409}{10.1103/PhysRevLett.88.170409}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/math-ph/0112032}{math-ph/0112032}}.\par\medskip
\bibitem[LSe05]{LSe05}E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason - {\it The Mathematics of the Bose Gas and its Condensation}, Oberwolfach Seminars, volume\-~34, Birkha\"user, 2005, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/cond-mat/0610117}{cond-mat/0610117}}.\par\medskip
\bibitem[LSY00]{LSY00}E.H. Lieb, R. Seiringer, J. Yngvason - {\it Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional}, Physical Review A, volume\-~61, issue\-~4, number\-~043602, 2000,\par\penalty10000
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\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
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\bibitem[NNe22]{NNe22}P.T. Nam, M. Napi\'orkowski, J. Ricaud, A. Triay - {\it Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime}, Analysis and PDE, volume\-~15, issue\-~6, pages\-~1585-1616, 2022,\par\penalty10000
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\bibitem[NRS16]{NRS16}P.T. Nam, N. Rougerie, R. Seiringer - {\it Ground states of large bosonic systems : the Gross–Pitaevskii limit revisited}, Analysis and PDE, volume\-~9, issue\-~2, pages\-~459-485, 2016,\par\penalty10000
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\bibitem[NT21]{NT21}P.T.\-~Nam, A.\-~Triay - {\it Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime}, arXiv preprint, 2021\par\penalty10000
arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2106.11949}{2106.11949}}.\par\medskip
\bibitem[Pi61]{Pi61}L.P. Pitaevskii - {\it Vortex lines in an imperfect Bose gas}, Soviet Physics JETP, volume\-~13, number\-~2, pages\-~451-454, 1961.\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
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\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
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