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Creators/Authors contains: "Boßmann, Lea"

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  1. ; ; ; (, Journal of Statistical Physics)
    Abstract 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 N $$d$$ d -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 $$(N-1)^{-1}N^{d\beta }v(N^\beta \cdot )$$ ( N - 1 ) - 1 N d β v ( N β · ) for $$\beta \in [0,\frac{1}{4d})$$ β ∈ [ 0 , 1 4 d ) . We derive a sequence of N -body functions which approximate the true many-body dynamics in $$L^2({\mathbb {R}}^{dN})$$ L 2 ( R dN ) -norm to arbitrary precision in powers of $$N^{-1}$$ 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. 
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