Medium effects and the shear viscosity of the dilute Fermi gas away from the conformal limit

We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=n{\lambda }^3/2$ is small. Here, $n$ is the density of the gas and $\lambda$ is the thermal wavelength of the fermions. At leading order in the fugacity expansion, the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order, medium effects modify the scattering amplitude as well as the quasiparticle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation side of the resonance, in agreement with the result of recent experiments.

Figure 1

Left panel: Scaled shear viscosity difference from unitarity $(\eta -{\eta }_{\infty })/{\eta }_{\infty }$ as a function of $x=1/\left(k_{F}a\right)$ for different values of $t=T/T_F$. The shear viscosity is computed from the in-medium cross section containing only the influence of $\mathrm{Re}\delta \Pi$. Furthermore, medium corrections to the quasiparticle energy and velocity are neglected. Right panel: shear viscosity $\eta$ scaled by the particle density $n$ from Eq. (4) as a function of $t$ for different values of $x$.

Figure 2

Scaled shear viscosity difference $(\eta -{\eta }_{\infty })/{\eta }_{\infty }$ as a function of $x=1/\left(k_{F}a\right)$ for different values of $t=T/T_F$. This figure shows the result of a systematic expansion to order $O\left({(\lambda /a)}^2\right)$ and $O\left(z\right(\lambda /a\left)\right)$; see Eq. (32).