High-temperature limit of the resonant Fermi gas

TL;DR

This paper investigates the high-temperature behavior of the resonant Fermi gas using a new diagrammatic virial expansion formalism, revealing a smooth crossover from fermionic to bosonic behavior and providing estimates for virial coefficients and thermodynamic properties.

Contribution

It introduces a novel diagrammatic approach to compute virial coefficients including effective range effects, enabling perturbative calculations at unitarity and accurate estimations of thermodynamic quantities.

Findings

Virial coefficients are computed near unitarity with effective range considerations.

The fourth virial coefficient at unitarity is close to experimental values.

Derived equations of state and spectral functions at high temperatures.

Abstract

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a new formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range $R^*$ in the interaction. In the limit where the thermal wavelength $\lambda \ll R^*$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\lambda/|a| \gg 1$ and $R^*/\lambda \gg 1$, we estimate the value of the fourth virial coefficient at unitarity for $R^*=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density and entropy, as well as the spectral function at high temperatures.