$\eta /s$ of the Normal Phase of Unitary Fermi Gas from $\epsilon$ Expansion

Abstract

Using $\epsilon$-expansion technique we compute $\eta /s$, where $\eta$ is the shear viscosity, $s$ is the entropy density, of the normal phase of unitary Fermi gas in $d=4-\epsilon$ dimensions to LO in $\epsilon$. We use kinetic theory approach and solve transport equations for medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\epsilon }^2$ which is LO. The LO result is temperature independent with $\eta /\mathrm{s}\simeq (0.11/{\epsilon }^2)(\hslash /{\mathrm{k}}_{\mathrm{B}}).$ The $d=3$ prediction for $\eta /\mathrm{s}$ exceeds the $\hslash /4\pi k_B$ bound by a factor of about $\mathrm{1.4.}$

Comments: 13 pages, 2 figures