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

Thursday, 26 October, 2017

Published in: 

arXiv:1710.09743

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

Author(s): 

Christian Brennecke
Phan Thành Nam
Marcin Napiórkowski
Benjamin Schlein