Virial coefficients for trapped Bose and Fermi gases beyond the unitary limit: AnS-matrix approach

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.

Two-dimensional Bose and Fermi gases beyond weak coupling

“…We now compare (34) with known results and experiments. From the scattering length definition given by (8) we see log √ α ≈ 2π/mg.…”

“…In the free theory, the series expansion of the poly-logarithm sLi 2 (sz) gives b n = s n+1 /n 2 . As explained in [34] our formalism gives the corrections to b 2 and b 3 : where k = |k| and σ = 1 for bosons and A1. Note that it changes sign at α ≈ 2.65.…”

Metastability of Bose and Fermi gases on the upper branch

“…For both bosons and fermions, the limit a s → ±∞ is the so-called unitary limit, where the theory is scale invariant. The unitary limit has been explored extensively within this formulation of statistical mechanics in [18][19][20], and will therefore not be discussed in this work. Although we will restrict our analysis of the upper branch to a s > 0, it is nevertheless important to mention that for bosons the upper branch phase is believed to extend smoothly across unitarity.…”