Fluctuations of N -particle quantum dynamics around the nonlinear Schrödinger equation
Brennecke, Christian1 ; Nam, Phan Thành2 ; Napiórkowski, Marcin3 ; Schlein, Benjamin1
1 Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2 Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, Germany
3 Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 5, pp. 1201-1235.
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We consider a system of N bosons interacting through a singular two-body potential scaling with N and having the form N3β−1V(Nβx), for an arbitrary parameter β∈(0,1). We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose–Einstein condensation in terms of a cubic nonlinear Schrödinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.

DOI : 10.1016/j.anihpc.2018.10.007
Mots-clés : Many-body quantum dynamics, Bogoliubov approximation, Nonlinear Schrödinger equation, Gross–Pitaevskii equation
Brennecke, Christian 1 ; Nam, Phan Thành 2 ; Napiórkowski, Marcin 3 ; Schlein, Benjamin 1

1 Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2 Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, Germany
3 Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland 
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     title = {Fluctuations of $N$-particle quantum dynamics around the nonlinear {Schr\"odinger} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Brennecke, Christian; Nam, Phan Thành; Napiórkowski, Marcin; Schlein, Benjamin. Fluctuations of $N$-particle quantum dynamics around the nonlinear Schrödinger equation. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 5, pp. 1201-1235. doi : 10.1016/j.anihpc.2018.10.007. http://www.numdam.org/articles/10.1016/j.anihpc.2018.10.007/

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