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

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 ($a_2^{(0)}=-\frac{1}{4\sqrt{2}}$) or fermions($a_2^{(0)}=\frac{1}{4\sqrt{2}}$), 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.

arXiv commentFinal published version revised according to comments; with more figures

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• The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics
• Joule-Thomson coefficient of ideal anyons within fractional exclusion statistics
• Three-dimensional correlated-fermion phase separation from analysis of the geometric mean of the individual susceptibilities
• Determination of Landau Fermi-liquid parameters of strongly interacting fermions by means of a nonlinear scaling transformation