Virial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach

TL;DR

This paper calculates virial coefficients for Bose and Fermi gases at finite temperature using an S-Matrix approach, considering two-body interactions beyond the unitary limit, including effects of trapping potentials.

Contribution

It introduces an approximation for virial coefficients considering only two-body processes applicable at high temperatures and low densities, extending analysis beyond the unitary limit.

Findings

First virial coefficients computed for the full scattering length range.

Second virial coefficient obtained exactly.

Analytical results derived for trapped gases using LDA.

Abstract

We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the Local Density Approximation - LDA, analytical results are obtained and the special case of the isotropic trap is discussed in detail.