Bulk viscosities for cold Fermi superfluids close to the unitary limit

TL;DR

This paper calculates the bulk viscosity coefficients of a cold Fermi superfluid near unitarity, revealing their dependence on phonon dispersion and conformal symmetry breaking at low temperatures.

Contribution

It provides the first detailed computation of bulk viscosity coefficients for non-relativistic superfluids near unitarity using kinetic theory and effective field theory.

Findings

All bulk viscosity coefficients vanish for linear phonon dispersion.

Non-zero bulk viscosity coefficient $B6_3$ appears with cubic phonon dispersion.

Bulk viscosities $3B6_1$ and $3B6_2$ depend on the inverse scattering length.

Abstract

We compute the coefficients of bulk viscosity for a non-relativistic superfluid corresponding to a fermionic system close to the unitarity limit. We consider the low temperature regime assuming that the transport properties of the system are dominated by phonons. To compute the coefficients of bulk viscosity we use kinetic theory in the relaxation time approximation and the low energy effective field theory of the corresponding system. We show that the three independent bulk viscosity coefficients, $\zeta_1, \zeta_2, \zeta_3$, associated with irreversible flows vanish for phonons with a linear dispersion law. Considering a phonon dispersion law with a cubic term in momentum we find that in the conformal limit $\zeta_1 = \zeta_2=0$, while $\zeta_3$ is non-zero. Including a conformal breaking term which arises for a large but finite s-wave scattering length, $a$, at the leading order in $1/a$ we obtain that $\zeta_1 \propto 1/a$ and $\zeta_2 \propto 1/a^2$.