Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

TL;DR

This paper derives explicit relations connecting thermodynamic properties and transport coefficients in unitary Fermi superfluids, accounting for superfluidity and pairing fluctuations, thereby enhancing understanding of superfluid behavior.

Contribution

It introduces new explicit relations between thermodynamics and transport in unitary Fermi superfluids, including effects of pairing fluctuations, advancing theoretical understanding.

Findings

Derived an explicit relation between pressure, chemical potential, and shear viscosity.

Established an approximate relation incorporating pairing fluctuations.

Provided insights into the link between equilibrium properties and transport in superfluids.

Abstract

The shear viscosity has been shown to be equal to the product of pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. By 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 flucutaions advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which can be otherwise difficult to measure.