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Bossmann, Lea; Pavlovic, Natasa; Pickl, Peter; Soffer, Avy (2020): Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons. In: Journal of Statistical Physics, Vol. 178, No. 6: pp. 1362-1396
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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 beta v(N beta center dot) for beta is an element of[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.