Bossmann, Lea; Pavlovic, Natasa; Pickl, Peter; Soffer, Avy
(2020):
Higher Order Corrections to the MeanField Description of the Dynamics of Interacting Bosons.
In: Journal of Statistical Physics, Vol. 178, No. 6: pp. 13621396

Full text not available from 'Open Access LMU'.
Abstract
In this paper, we introduce a novel method for deriving higher order corrections to the meanfield description of the dynamics of interacting bosons. More precisely, we consider the dynamics of Nddimensional bosons for large N. The bosons initially form a BoseEinstein condensate and interact with each other via a pair potential of the form (N1)1Nd beta v(N beta center dot) for beta is an element of[0,14d). We derive a sequence of Nbody functions which approximate the true manybody dynamics in L2(RdN)norm to arbitrary precision in powers of N1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.