The free energy of the two-dimensional dilute Bose gas. II. Upper bound
| Autor: | Mayer, Simon, Seiringer, Robert |
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| Rok vydání: | 2020 |
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| Zdroj: | J. Math. Phys. 61, 061901 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0005950 |
| Popis: | We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit volume differs from the one of the non-interacting system by at most $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$ to leading order, where $a$ is the scattering length of the two-body interaction potential, $\rho$ is the density, $\beta$ the inverse temperature and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved in \cite{DMS19} this shows equality in the asymptotic expansion. Comment: LaTeX, 24 pages; final version, to appear in J. Math. Phys |
| Databáze: | arXiv |
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