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.

Final published version revised according to comments; with more figures

References in corpus (4)

• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Measurement of the Entropy and Critical Temperature of a Strongly Interacting Fermi Gas
• Ultracold two-component Fermi gases with a magnetic field gradient near a Feshbach resonance
• Quantum rearrangement and self-consistent BCS-BEC crossover thermodynamics

Cited by in corpus (3)

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