Viscosity spectral functions of the dilute Fermi gas in kinetic theory

Understand

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.