The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

TL;DR

This paper applies fractional exclusion statistics to analyze the thermodynamics of a trapped unitary Fermi gas at finite temperatures, comparing theoretical predictions with experimental data and examining heat capacity behavior.

Contribution

It introduces a fractional exclusion statistics approach to study finite-temperature thermodynamics of a trapped unitary Fermi gas, providing new insights and comparisons with experiments.

Findings

Reasonable agreement between theory and experiment for entropy and energy per particle.

Analysis of isochore heat capacity behavior in the fractional exclusion statistics framework.

Discrepancies in chemical potential behavior compared to experimental data.

Abstract

We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.