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arXiv · 2507.20877

A new upper bound on the specific free energy of dilute Bose gases

Giulia Basti·Chiara Boccato·Serena Cenatiempo·Andreas Deuchert
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Abstract

We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system by the correction term $4 \pi \frak{a} (2 \rho^2 - [\rho - \rho_{\textsf{c}}(\beta)]^2_+ )$. Here, $\frak{a}$ denotes the scattering length of the interaction potential, $\rho_{\textsf{c}}(\beta)$ the critical density for Bose-Einstein condensation of the non-interacting gas and $[\cdot]_+=\max\{0,\cdot\}$. This result was previously established by Yin in [37]. Our proof applies to a broader class of interaction potentials, yields a better rate, and we believe it has potential for further extensions.

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Giulia Basti, Chiara Boccato, Serena Cenatiempo, Andreas Deuchert. 2025-07-28. A new upper bound on the specific free energy of dilute Bose gases. https://arxiv.org/abs/2507.20877

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