The virial equation of state for unitary fermion thermodynamics with non-Gaussian correlations

TL;DR

This paper derives the virial equation of state for a unitary Fermi gas, incorporating non-Gaussian correlations and high-order perturbations, revealing novel thermodynamic behaviors and calculating complex virial coefficients up to the fourth order.

Contribution

It introduces a comprehensive calculation of virial coefficients for the unitary Fermi gas considering non-local correlations and quantum effects, extending beyond mean-field theories.

Findings

Second virial coefficient of the Fermi gas at unitarity is zero.

Virial coefficients are proportional to those of ideal quantum gases with integer ratios.

The thermodynamics follow classical Boyle's law in the Boltzmann regime.

Abstract

We study the roles of the dynamical high order perturbation and statistically non-linear infrared fluctuation/correlation in the virial equation of state for the Fermi gas in the unitary limit. Incorporating the quantum level crossing rearrangement effects, the spontaneously generated entropy departing from the mean-field theory formalism leads to concise thermodynamical expressions. The dimensionless virial coefficients with complex non-local correlations are calculated up to the fourth order for the first time. The virial coefficients of unitary Fermi gas are found to be proportional to those of the ideal quantum gas with integer ratios through a general term formula. Counterintuitively, contrary to those of the ideal bosons ($a^{(0)}_2=-\frac{1}{4 \sqrt{2}}$) or fermions($a^{(0)}_2=\frac{1}{4 \sqrt{2}}$), the second virial coefficient $a_2$ of Fermi gas at unitarity is found to be equal to zero. With the vanishing leading order quantum correction, the BCS-BEC crossover thermodynamics manifests the famous pure classical Boyle's law in the Boltzmann regime. The non-Gaussian correlation phenomena can be validated by studying the Joule-Thomson effect.