Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

Abstract

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 associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low temperature transport associated with the quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. Interestingly, we find that the transport properties of strict BCS and Bogoliubov superfluids have very similar structures, albeit with different quasi-particle dispersion relations. While there is a dramatic contrast between the power law and exponential temperature dependence for $\eta$ alone, the ratio $\eta /s$ for both systems is more similar. Specifically we find the same linear dependence (on the ratio of temperature $T$ to inverse lifetime $\gamma (T)$) with $\eta /s\propto T/\gamma (T)$, corresponding to imperfect fluidity. By contrast, near the unitary limit of BCS-BEC superfluids a very different behavior results, which is more consistent with near-perfect fluidity.

v2: 8 pages, 3 figures

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