Shear Viscosity of a Unitary Fermi Gas

We present an ab initio determination of the shear viscosity $\eta$ of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio $\eta /s$. The minimum of $\eta /s$ appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being $(\eta /s{)}_{\min }\approx 0.2\hslash /k_B$, which is close the Kovtun-Son-Starinets universal value $\hslash /(4\pi k_B)$.

Figure 1

The dimensionless static shear viscosity $\eta /n$ as a function of $T/{\epsilon }_F$ for an $8^3$ lattice (red) squares and ${10}^3$ lattice solid (blue) circles. The error bars only represent the stability of the combined (SVD and MEM) inversion procedure with respect to changes in the algorithm parameters. The (green) line depicts the prediction of kinetic theory [12]. For comparison, recent results of the $T$-matrix theory produced by Enss et al., are plotted as open (purple) circles [15].

Figure 2

Entropy per particle as a function of $T/{\epsilon }_F$ for the $8^3$ lattice in (red) squares and ${10}^3$ lattice in (blue) circles. The entropy per particle extracted from the recent MIT measurement [35] is plotted with (black) crosses.

Figure 3

Ratio of the shear viscosity to entropy density $\eta /s$ as a function of $T/{\epsilon }_F$ for an $8^3$ lattice (red) squares and ${10}^3$ lattice (blue) circles. The error bars only represent the stability of the combined (SVD and MEM) inversion procedure with respect to the change of algorithm parameters and do not include systematic errors of the entropy determination. Results of the $T$-matrix theory are plotted by open (purple) circles [15]. In the high- and low-temperature regimes, known asymptotics are depicted: for $T>0.3{\epsilon }_F$ the prediction of kinetic theory [12] as a solid (green) line, and for $T<0.2{\epsilon }_F$ the contribution from phonon excitations [13] as a dotted (brown) line. The KSS bound appears as a dashed black line.