Bulk Viscosity and Conformal Symmetry Breaking in the Dilute Fermi Gas near Unitarity

The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute, in the high temperature limit, the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio $(P-2/3\mathcal{E})/P$, where $P$ is the pressure and $\mathcal{E}$ is the energy density. At high temperature this ratio scales as $z$\lambda${}/a$, where $z$ is the fugacity, $$\lambda${}$ is the thermal wavelength, and $a$ is the scattering length. We show that the bulk viscosity $$\zeta${}$ scales as the second power of this parameter, $$\zeta${}$\sim${}(z$\lambda${}/a{)}^{2}{$\lambda${}}^{-3}$.