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

Understand

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 $(2P-\rho c_s^2)/P\sim z/[\log(T/E_B)]^2$, and that the bulk viscosity $\zeta$ scales as $\zeta/\eta \sim z^2/[\log(T/E_B)]^6$.
• 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.