Transport Coefficients of a Normal Fermi Gas at Unitarity

C. J. Pethick

C. J. Pethick

Erik M. Weiler

Soudabe Nasirimoghadam, F. Nabipoor, Maryam Khademi Dehkordi +1 more

Thomas Schäfer

We compute second-order transport coefficients of the dilute Fermi gas at unitarity. The calculation is based on kinetic theory and the Boltzmann equation at second order in the Knudsen expansion. The second-order transport coefficients describe the shear stress relaxation time, nonlinear terms in the strain-stress relation, and nonlinear couplings between vorticity and strain. An exact calculation in the dilute limit gives ${\ensuremath{\tau}}_{R}=\ensuremath{\eta}/P$, where ${\ensuremath{\tau}}_{R}$ is the shear stress relaxation time, $\ensuremath{\eta}$ is the shear viscosity, and $P$ is pressure. This relation is identical to the result obtained using the Bhatnagar-Gross-Krook approximation to the collision term, but other transport coefficients are sensitive to the exact collision integral.

Daichi Kagamihara, Daisuke Inotani, Yoji Ohashi

We theoretically investigate the shear viscosity $η$ in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent $T$-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature $T_{\rm c}$. We show that, while $η$ diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of $η$ is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a $^6$Li Fermi gas. In the weak-coupling BCS regime, we also find that $η$ exhibits anomalous temperature dependence near $T_{\rm c}$, which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.