Shear viscosity of a superfluid Fermi gas in the unitarity limit

TL;DR

This paper calculates the shear viscosity of a superfluid Fermi gas at unitarity, revealing a temperature-dependent scaling and suggesting a minimum near the critical temperature, with implications for quantum bounds on viscosity.

Contribution

It provides a theoretical analysis of shear viscosity in a superfluid Fermi gas at unitarity, including low and high temperature behaviors and their implications.

Findings

Viscosity scales as xi^5/T^5 at low temperatures

Viscosity has a minimum near the critical temperature T_c

Minimum viscosity-to-entropy ratio is within a factor of 5 of the quantum bound

Abstract

We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature T limit the shear viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the chemical potential and the Fermi energy, mu=xi E_F. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature T_c. A naive extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of ~ 5 of the proposed lower bound hbar/(4\pi k_B).