Comparative study of the finite-temperature thermodynamics of a unitary Fermi gas

TL;DR

This paper analytically investigates the finite-temperature thermodynamics of a unitary Fermi gas using a quasi-linear approximation, comparing results with generalized exclusion statistics and highlighting differences in effective fermion mass predictions.

Contribution

It introduces a quasi-linear approximation approach to analyze thermodynamics of a unitary Fermi gas and compares it with generalized exclusion statistics, providing new insights into effective mass behavior.

Findings

Ground state energy matches previous results.

Quasi-linear approximation predicts effective mass greater than one.

Comparison with generalized exclusion statistics shows differing effective mass values.

Abstract

We study the finite-temperature thermodynamics of a unitary Fermi gas. The chemical potential, energy density and entropy are given analytically with the quasi-linear approximation. The ground state energy agrees with previous theoretical and experimental results. Recently, the generalized exclusion statistics is applied to the discussion of the finite-temperature unitary Fermi gas thermodynamics. A concrete comparison between the two different approaches is performed. Emphasis is made on the behavior of the entropy per particle. In physics, the slope of entropy gives the information for the effective fermion mass $m^*/m$ in the low temperature strong degenerate region. Compared with $m^*/m \approx 0.70<1$ given in terms of the generalized exclusion statistics, our quasi-linear approximation determines $m^*/m\approx 1.11>1$.