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

A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).

Preprint | Draft | English
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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 $\beta \rho \gtrsim 1$.
Publishing Year
Date Published
2019-10-08
Journal Title
arXiv:1910.03372
Page
61
IST-REx-ID

### Cite this

Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:191003372.
Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. ArXiv:1910.03372. ArXiv.
Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372. ArXiv, n.d.
A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” arXiv:1910.03372. ArXiv.
Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372.
Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372, ArXiv.