# High-temperature expansion of the viscosity in interacting quantum gases

## TL;DR

This paper calculates the high-temperature shear and bulk viscosity spectral functions of an interacting Fermi gas using a quantum virial expansion and diagrammatic field theory, revealing broad spectra, bound states, and nonanalytic bulk viscosity behavior.

## Contribution

It provides a detailed high-temperature expansion of viscosity spectral functions with analytic continuation, including bound-state effects and nonanalytic bulk viscosity dependence.

## Key findings

- Spectral functions show a broad continuous spectrum at all frequencies.
- Bound-state contributions appear above the dimer-breaking energy.
- Bulk viscosity exhibits nonanalytic dependence on scattering length.

## Abstract

We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter $z=e^{\beta \mu}$, which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theoretic framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides a possible zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an additional bound-state contribution for frequencies larger than the dimer-breaking energy. Our results are consistent with various sum rules and universal high-frequency tails. In the low-frequency limit, the shear viscosity spectral function is recast as a collision integral, which reproduces known results for the static shear viscosity from kinetic theory. Our findings for the static bulk viscosity of a Fermi gas near unitarity, however, show a nonanalytic dependence on the scattering length, at variance with kinetic theory.