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, $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$, respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity $\ensuremath{\eta}$ and the normal-fluid density ${\ensuremath{\rho}}_{n}$; sum rules for $\ensuremath{\zeta}(\ensuremath{\omega})$ and $\ensuremath{\eta}(\ensuremath{\omega})$ and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for $\ensuremath{\eta}(\ensuremath{\omega})$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$. We use our sum rules to show that, at unitarity, $\ensuremath{\zeta}(\ensuremath{\omega})$ is identically zero and thus relate $\ensuremath{\eta}(\ensuremath{\omega})$ to density-density correlations. We predict that frequency-dependent shear viscosity $\ensuremath{\eta}(\ensuremath{\omega})$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.
The scattering properties of spin-polarized Fermi gases are dominated by
p-wave interactions. Besides their inherent angular dependence, these interactions differ from their
s-wave counterparts as they also require the presence of a finite effective range in order to understand the low-energy properties of the system. In this article we examine how the shear viscosity and thermal conductivity of a three-dimensional spin-polarized Fermi gas in the normal phase depend on the effective range and the scattering volume in both the weakly and the strongly interacting limits. We show that, although the shear viscosity and the thermal conductivity both explicitly depend on the effective range near resonance, the Prandtl number which parametrizes the ratio of momentum to thermal diffusivity does not have an explicit interaction dependence both at resonance and for weak interactions in the low-energy limit. In contrast to
s-wave systems,
p-wave scattering exhibits an additional resonance at weak attraction from a quasi-bound state at positive energies, which leads to a pronounced dip in the shear viscosity at specific temperatures.