Bulk viscosities for cold Fermi superfluids close to the unitary limit

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, $ζ_1, ζ_2, ζ_3$, 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 $ζ_1 = ζ_2=0$, while $ζ_3$ 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 $ζ_1 \propto 1/a$ and $ζ_2 \propto 1/a^2$.