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arXiv · 1910.03372

The free energy of the two-dimensional dilute Bose gas. I. Lower bound

Andreas Deuchert·Simon Mayer·Robert Seiringer
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Abstract

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot \}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$.

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Andreas Deuchert, Simon Mayer, Robert Seiringer. 2019-10-08. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. https://doi.org/10.1017/fms.2020.17

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