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arXiv · 2307.01113

Pressure of a dilute spin-polarized Fermi gas: Lower bound

Asbjørn Bækgaard Lauritsen·Robert Seiringer
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Abstract

We consider a dilute spin-polarized Fermi gas at positive temperature in dimensions $d\in\{1,2,3\}$. We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^d\rho^{2+2/d}$, where $a$ is the $p$-wave scattering length of the repulsive interaction and $\rho$ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260).

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Asbjørn Bækgaard Lauritsen, Robert Seiringer. 2023-07-03. Pressure of a dilute spin-polarized Fermi gas: Lower bound. https://doi.org/10.1017/fms.2024.56

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