Viscosity of strongly interacting quantum fluids: spectral functions and sum rules

Abstract

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 ${\rho }_n$; 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 $S(\mathbf{q},\omega )$. We use our sum rules to show that, at unitarity, $\zeta (\omega )$ is identically zero and thus relate $\eta (\omega )$ to density-density correlations. We predict that frequency-dependent shear viscosity $\eta (\omega )$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.

Comments: Published version