# Bulk viscosity and contact correlations in attractive Fermi gases

## TL;DR

This paper investigates how pair fluctuations influence bulk viscosity in attractive Fermi gases, revealing deviations from scale invariance and effects near the superfluid transition, with numerical results across the BEC-BCS crossover.

## Contribution

It provides the first numerical Luttinger-Ward calculations of contact correlations and bulk viscosity throughout the BEC-BCS crossover, highlighting the role of pair fluctuations.

## Key findings

- Bulk viscosity is linked to contact density correlations.
- Pair fluctuations break scale invariance, affecting viscosity.
- Bulk viscosity peaks near the superfluid transition.

## Abstract

The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity $\zeta/\eta$ is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics and sound attenuation.