The free energy of the two-dimensional dilute Bose gas. II. Upper bound

S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).


Journal Article | Published | English

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Abstract
We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion.
Publishing Year
Date Published
2020-06-22
Journal Title
Journal of Mathematical Physics
Volume
61
Issue
6
Article Number
061901
ISSN
IST-REx-ID

Cite this

Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 2020;61(6). doi:10.1063/5.0005950
Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics, 61(6). https://doi.org/10.1063/5.0005950
Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics 61, no. 6 (2020). https://doi.org/10.1063/5.0005950.
S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” Journal of Mathematical Physics, vol. 61, no. 6, 2020.
Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6).
Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics, vol. 61, no. 6, 061901, AIP, 2020, doi:10.1063/5.0005950.
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