The Thermodynamic Pressure of a Dilute Fermi Gas

TL;DR

This paper derives the leading order correction to the thermodynamic pressure of a dilute Fermi gas due to interactions, showing it depends on the scattering length and holds across various temperatures.

Contribution

It provides a rigorous derivation of the interaction correction to the pressure for dilute Fermi gases with small-range interactions, valid at finite temperatures.

Findings

Pressure correction proportional to scattering length

Applicable to any repulsive interaction including hard cores

Uniform validity for temperatures up to Fermi temperature

Abstract

We consider a gas of fermions with non-zero spin at temperature $T$ and chemical potential $\mu$. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as $T$ is of the same order as the Fermi temperature, or smaller.