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Brennecke, Christian; Phan Thanh, Nam; Napiorkowski, Marcin and Schlein, Benjamin (2019): Fluctuations of N-particle quantum dynamics around the nonlinear Schrodinger equation. In: Annales De L Institut Henri Poincare-Analyse Non Lineaire, Vol. 36, No. 5: pp. 1201-1235

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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 N3 beta-1 V(N(beta)x), for an arbitrary parameter beta is an element of (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 Schrodinger 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. (C) 2018 Elsevier Masson SAS. All rights reserved.

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