Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

TL;DR

This paper investigates the shear viscosity to entropy density ratio in bosonic and fermionic superfluids, revealing how their fluidity properties vary with temperature and interaction regimes, and highlighting conditions for near-perfect fluidity.

Contribution

It provides a comparative analysis of shear viscosity and fluidity in bosonic and fermionic superfluids using microscopic transport theories, including BCS and Bogoliubov approximations.

Findings

Similar transport structures in BCS and Bogoliubov superfluids despite different quasi-particle dispersions

The ratio η/s scales linearly with T/γ(T), indicating imperfect fluidity in general

Near the unitary limit, superfluids exhibit behavior consistent with near-perfect fluidity

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.