Thermal Conductivity and Sound Attenuation in Dilute Atomic Fermi Gases

TL;DR

This paper calculates thermal conductivity and sound attenuation in dilute atomic Fermi gases across the superfluid transition, revealing temperature-dependent scaling laws and implications for measuring shear viscosity.

Contribution

It provides the first detailed kinetic theory calculations of thermal conductivity and sound attenuation in both normal and superfluid phases of dilute Fermi gases.

Findings

Thermal conductivity scales as T^{3/2} above T_c

Thermal conductivity scales as T^{2} below T_c

Sound attenuation is dominated by shear viscosity near T_c

Abstract

We compute the thermal conductivity and sound attenuation length of a dilute atomic Fermi gas in the framework of kinetic theory. Above the critical temperature for superfluidity, T_c, the quasi-particles are fermions, whereas below T_c, the dominant excitations are phonons. We calculate the thermal conductivity in both cases. We find that at unitarity the thermal conductivity \kappa in the normal phase scales as \kappa ~ T^{3/2}. In the superfluid phase we find \kappa ~ T^{2}. At high temperature the Prandtl number, the ratio of the momentum and thermal diffusion constants, is 2/3. The ratio increases as the temperature is lowered. As a consequence we expect sound attenuation in the normal phase just above T_c to be dominated by shear viscosity. We comment on the possibility of extracting the shear viscosity of the dilute Fermi gas at unitarity using measurements of the sound absorption length.