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

TL;DR

This paper establishes a rigorous lower bound on the pressure of a dilute spin-polarized Fermi gas at positive temperature, incorporating interaction effects characterized by the p-wave scattering length, valid across various repulsive interactions.

Contribution

It provides the first rigorous lower bound on the pressure of an interacting dilute Fermi gas, including explicit leading-order correction terms, using a fermionic cluster expansion.

Findings

Pressure bounded from below by free gas pressure plus explicit interaction term

Results valid for a wide range of repulsive interactions, including hard core

Applicable at temperatures up to the Fermi temperature

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).