Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas

We study two observables related to the anomalous breaking of scale invariance in a dilute two-dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two-dimensional gas in the high-temperature limit. We show that the anomaly in the speed of sound scales as $(2P-\rho c_s^2)/P\sim z/{\left[\ln (T/E_B)\right]}^2$ and that the bulk viscosity $\zeta$ scales as $\zeta /\eta \sim z^2/{\left[\ln (T/E_B)\right]}^6$. Here, $P$ is the pressure, $c_s^2$ is the speed of sound, $\eta$ is the shear viscosity, $z$ is the fugacity, and $E_B$ is the two-body binding energy. We show that our results are consistent with the experimental results of Vogt, Feld, Fröhlich, Pertot, Koschorreck, and Köhl [ Phys. Rev. Lett. 108, 070404 (2012)]. Vogt et al. reported a frequency shift $\delta \omega /\omega$ of the order of a few percent and a damping rate smaller than the background rate $\Gamma /{\omega }_0\sim 5\%$.