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

TL;DR

This paper establishes an upper bound on the pressure of a dilute spin-polarized Fermi gas, capturing the main correction due to repulsive interactions, aligning with previous lower bounds and advancing theoretical understanding of quantum gases.

Contribution

It provides a rigorous upper bound on the pressure correction in a dilute spin-polarized Fermi gas, matching the known lower bound and refining theoretical predictions.

Findings

Upper bound on pressure correction of order a^3 rho^{8/3}

Correction depends on temperature and p-wave scattering length

Results match the lower bound from prior work

Abstract

We prove an upper bound on the pressure of a dilute fully spin-polarized Fermi gas capturing the leading correction to the pressure of a free gas resulting from repulsive interactions. This correction is of order $a^3\rho^{8/3}$, with $a$ the $p$-wave scattering length of the interaction and $\rho$ the particle density, depends on the temperature and matches the corresponding lower bound of [arXiv:2307.01113].