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

Abstract

We study the roles of the dynamical high order perturbation and statistically non-linearinfrared fluctuation/correlation in the virial equation of state for the Fermi gas in theunitary limit. Incorporating the quantum level crossing rearrangement effects, thespontaneously generated entropy departing from the mean-field theory formalism leads toconcise thermodynamical expressions. The dimensionless virial coefficients with complexnon-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 thoseof the ideal quantum gas with integer ratios through a general term formula.Counterintuitively, contrary to those of the ideal bosons () or fermions (), the second virial coefficient a2 of Fermi gas at unitarity is found to be equal to zero. With the vanishing leadingorder quantum correction, the BCS–BEC crossover thermodynamics manifests thefamous pure classical Boyle’s law in the Boltzmann regime. The non-Gaussiancorrelation phenomena can be validated by studying the Joule–Thomson effect.