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

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 nonrelativistic 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, nonperturbative 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 (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for eta(omega) and the dynamic structure factor S(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.