Third- and fourth-order virial coefficients of harmonically trapped fermions in a semiclassical approximation

Abstract

Using a leading-order semiclassical approximation, we calculate the third-and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency and coupling strength. Our simple, analytic results for the interaction-induced changes ∆b3 and ∆b4 agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of threedimensional Fermi gases. arXiv:1908.00070v1 [cond-mat.quant-gas]

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

“…As Refs. [10][11][12] have shown, this seemingly crude approximation provides surprisingly good answers, especially at weak coupling, and is therefore useful toward examining the virial expansion in an analytic fashion. Below, we give two explicit examples of the application of our approximation to the calculation of virial coefficients.…”

“…[11], the NLO-SCLA was explored up to b 7 , displaying the convergence properties up to the unitary point (in 3D) and in Ref. [12] the LO-SCLA was used for systems in a harmonic trap, showing that the approximation can capture the dependence on the trap frequency ω. In both cases, the analytic dependence of virial coefficients on the dimension was obtained, as will be the case here.…”

Thermodynamics of rotating quantum matter in the virial expansion

“…respectively the strong-and weak-coupling limits). Previous explorations of this approximation, by us and others [21][22][23]28], indicate that LO-level results (the socalled semiclassical approximation) for trapped systems are not only qualitatively but also quantitatively correct at weak coupling.…”

“…The use of ∆b 2 as a physical quantity to renormalize the coupling constant was advocated in Refs. [21][22][23].…”

“…To that end, we use the virial expansion and implement a coarse temporal lattice approximation recently put forward in Refs. [21][22][23]. The approximation allows us to bypass the requirement of solving the n-body problem to access the n-th order virial coefficient, which will be essential to address the effects of interactions.…”