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

2017/10/26 by Brennecke, Christian, Nam, Phan Thành, Napiórkowski, Marcin +1
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1710.09743

Abstract

We consider a system of N bosons interacting through a singular two-body potential scaling with N and having the form N^3β-1 V (N^βx), 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.

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