Fluctuations of $N$-particle quantum dynamics around the nonlinear Schrödinger equation

Christian Brennecke; Phan Thành Nam; Marcin Napiórkowski; Benjamin Schlein

doi:10.1016/j.anihpc.2018.10.007

JournalsaihpcVol. 36, No. 5pp. 1201–1235

Fluctuations of $N$ -particle quantum dynamics around the nonlinear Schrödinger equation

Christian Brennecke
Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
Phan Thành Nam
Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, Germany
Marcin Napiórkowski
Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
Benjamin Schlein
Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

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Abstract

We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3 β - 1} V (N^{β} x)$ , for an arbitrary parameter $β \in (0, 1)$ . 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.

Cite this article

Christian Brennecke, Phan Thành Nam, Marcin Napiórkowski, Benjamin Schlein, Fluctuations of $N$ -particle quantum dynamics around the nonlinear Schrödinger equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 5, pp. 1201–1235

DOI 10.1016/J.ANIHPC.2018.10.007