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, ζ(ω) and η(ω), respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity η and the normal-fluid density ρₙ; sum rules for ζ(ω) and η(ω) and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for η(ω) and the dynamic structure factor S(q,ω). We use our sum rules to show that, at unitarity, ζ(ω) is identically zero and thus relate η(ω) to density-density correlations. We predict that frequency-dependent shear viscosity η(ω) of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.