Edward Taylor and Mohit Randeria

The Ohio State University The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of emph{non-relativistic} quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $zeta(omega)$ and $eta(omega)$ respectively, to derive exact, non-perturbative results. Our results include: a microscopic connection between the shear viscosity $eta$ and the normal fluid density $ ho_n$; sum rules for $zeta(omega)$ and $eta(omega)$ and their evolution through the BCS-BEC crossover; universal high-frequency tails for $eta(omega)$ and the dynamic structure factor $S({f q}, omega)$. We use our sum rules to show that, at unitarity, $zeta(omega)$ is identically zero and thus relate $eta(omega)$ to density-density correlations.