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In this paper we address the ratio of the shear viscosity to entropy density$\eta/s$ in bosonic and fermionic superfluids. A small $\eta/s$ is associatedwith nearly perfect fluidity, and more general measures of the fluidityperfection/imperfection are of wide interest to a number of communities. We usea Kubo approach to concretely address this ratio via low temperature transportassociated with the quasi-particles. Our analysis for bosonic superfluidsutilizes the framework of the one-loop Bogoliubov approximation, whereas forfermionic superfluids we apply BCS theory and its BCS-BEC extension.Interestingly, we find that the transport properties of strict BCS andBogoliubov superfluids have very similar structures, albeit with differentquasi-particle dispersion relations. While there is a dramatic contrast betweenthe power law and exponential temperature dependence for $\eta$ alone, theratio $\eta/s$ for both systems is more similar. Specifically we find the samelinear dependence (on the ratio of temperature $T$ to inverse lifetime$\gamma(T)$) with $\eta/s \propto T/\gamma(T)$, corresponding to imperfectfluidity. By contrast, near the unitary limit of BCS-BEC superfluids a verydifferent behavior results, which is more consistent with near-perfectfluidity.

Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids