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

L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics (2020).

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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)−1Ndβv(Nβ·)forβ∈[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.
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2020-02-21
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Journal of Statistical Physics
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Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. 2020. doi:10.1007/s10955-020-02500-8
Bossmann, L., Pavlović, N., Pickl, P., & Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. https://doi.org/10.1007/s10955-020-02500-8
Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” Journal of Statistical Physics, 2020. https://doi.org/10.1007/s10955-020-02500-8.
L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” Journal of Statistical Physics, 2020.
Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics.
Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” Journal of Statistical Physics, Springer Nature, 2020, doi:10.1007/s10955-020-02500-8.
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