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

TL;DR

This paper uses an epsilon-expansion and kinetic theory to compute the shear viscosity to entropy density ratio of a unitary Fermi gas in non-integer dimensions, revealing it exceeds the quantum bound in three dimensions.

Contribution

It provides a leading-order epsilon-expansion calculation of eta/s for the normal phase of a unitary Fermi gas, including collision integrals to LO in epsilon.

Findings

LO eta/s is temperature independent.

Predicted eta/s in 3D exceeds the quantum bound by 1.4.

Method employs kinetic theory and transport equations.

Abstract

Using $\varepsilon$-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 $d=4-\varepsilon$ dimensions to LO in $\varepsilon$. We use kinetic theory approach and solve transport equations for medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to $\varepsilon^2$ which is LO. The LO result is temperature independent with $\eta/\rm s\simeq (0.11/\varepsilon^2)(\hbar/k_B).$ The $d=3$ prediction for $\eta/\rm s$ exceeds the $\hbar/4 \pi k_B$ bound by a factor of about $1.4.$