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arXiv · 1905.06164

Higher order corrections to the mean-field description of the dynamics of interacting bosons

Lea Boßmann·Nataša Pavlović·Peter Pickl·Avy Soffer
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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 $N$ $d$-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 $(N-1)^{-1}N^{d\beta}v(N^\beta\cdot)$ for $\beta\in[0,\frac{1}{4d})$. We derive a sequence of $N$-body functions which approximate the true many-body dynamics in $L^2(\mathbb{R}^{d N})$-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.

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Lea Boßmann, Nataša Pavlović, Peter Pickl, Avy Soffer. 2019-05-15. Higher order corrections to the mean-field description of the dynamics of interacting bosons. https://doi.org/10.1007/s10955-020-02500-8

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