Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons

Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096.


Journal Article | Epub ahead of print | English

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Author
Deuchert, Andreas; Seiringer, RobertIST Austria
Department
Abstract
We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions.
Publishing Year
Date Published
2021-05-05
Journal Title
Journal of Functional Analysis
Acknowledgement
Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.
Volume
281
Issue
6
Article Number
109096
ISSN
eISSN
IST-REx-ID

Cite this

Deuchert A, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 2021;281(6). doi:10.1016/j.jfa.2021.109096
Deuchert, A., & Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109096
Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109096.
A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons,” Journal of Functional Analysis, vol. 281, no. 6. Elsevier, 2021.
Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096.
Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis, vol. 281, no. 6, 109096, Elsevier, 2021, doi:10.1016/j.jfa.2021.109096.
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