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 178 (2020) 1362–1396.

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Author
Bossmann, LeaIST Austria ; Pavlović, Nataša; Pickl, Peter; Soffer, Avy
Department
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.
Publishing Year
Date Published
2020-02-21
Journal Title
Journal of Statistical Physics
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria). L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello Porta for helpful discussions. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1. Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and P.P. thank A.S. for his hospitality at CCNU.
Volume
178
Page
1362-1396
ISSN
eISSN
IST-REx-ID

Cite this

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;178:1362-1396. 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. Springer Nature. 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. Springer Nature, 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, vol. 178. Springer Nature, pp. 1362–1396, 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. 178, 1362–1396.
Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” Journal of Statistical Physics, vol. 178, Springer Nature, 2020, pp. 1362–96, doi:10.1007/s10955-020-02500-8.
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