Viscosity spectral functions of the dilute Fermi gas in kinetic theory

TL;DR

This paper calculates the viscosity spectral function of a dilute Fermi gas across different scattering lengths using kinetic theory, revealing characteristic peaks and their dependence on momentum and interaction strength.

Contribution

It provides a detailed kinetic theory computation of the viscosity spectral function for the dilute Fermi gas, including the unitarity limit, highlighting the structure and width of spectral peaks.

Findings

Diffusive peak in the shear channel with width $ o (2 ext{energy density})/(3 ext{shear viscosity})$

Sound peak observed in the longitudinal channel

Spectral function approaches collisionless limit at finite momentum

Abstract

We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length $a$, including the unitarity limit $a\to\infty$. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is $\omega_0\simeq (2\epsilon)/(3\eta)$ where $\epsilon$ is the energy density and $\eta$ is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of order $\omega_0\sim k(T/m)^{1/2}$.