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

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 s...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Lauritsen, Asbjørn Bækgaard, Seiringer, Robert
Format: Article
Language:English
Subjects:
Dilution
Fermi gases
Lower bounds
Particle density (concentration)
Wave scattering
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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).
ISSN:2331-8422
DOI:10.48550/arxiv.2307.01113