The shear viscosity has been shown to be equal to the product of the pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. Using the mean-field BCS-Leggett theory with a gauge-invariant linear response theory for unitary Fermi superfluids, we present an explicit relation between thermodynamic quantities, including the pressure and chemical potential, and transport coefficients, including the shear viscosity, superfluid density, and anomalous shear viscosity from momentum transfer via Cooper pairs. The relation is modified when pairing fluctuations associated with noncondensed Cooper pairs are considered. Within a pairing fluctuation theory consistent with the BCS-Leggett ground state, we found an approximate relation for unitary Fermi superfluids. The exact mean-field relation and the approximate one with pairing fluctuations advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which otherwise can be difficult to measure.

• Received 22 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.033638