Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons - Boßmann, Lea; Pavlović, Nataša; Pickl, Peter; Soffer, Avy (Journal of Statistical Physics, 2020)
In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of Nd-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N- 1) - 1Nd βv(Nβ·) for β∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN) -norm to arbitrary precision in powers of N- 1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.
CRIS-Team Scopus Importer:2024-10-02
Keywords: Bose-Einstein condensation; Many-body quantum dynamics; Mean-field scaling; Norm approximation