Viscosity spectral functions of the dilute Fermi gas in kinetic theory

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 ${\omega }_0\simeq (2ϵ)/(3\eta )$ where $ϵ$ 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 ${\omega }_0\sim k(T/m{)}^{1/2}$.

Comments: 15 pages, 6 figures