Shear viscosity of a superfluid Fermi gas in the unitarity limit

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 ξ⁵∕T⁵, where the universal parameter ξ relates the chemical potential and the Fermi energy, μ=ξεF. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature Tc. A na\"{}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of ~5 of the proposed bound η∕s≥∕(4πkB).