# Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow

## TL;DR

This study measures how the shear viscosity of a unitary Fermi gas varies with density and temperature using hydrodynamic flow data, revealing a minimum near the critical temperature.

## Contribution

It introduces a generalized hydrodynamic framework to accurately determine shear viscosity and its temperature dependence in a unitary Fermi gas.

## Key findings

- Shear viscosity to particle density ratio at T_c is 0.41±0.11.
- Shear viscosity to entropy density ratio has a minimum of 0.50±0.10 above T_c.
- The method ensures a smooth transition between fluid dynamic and ballistic regimes.

## Abstract

We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph et al. and measurements of the equation of state by Ku et al. We find that the shear viscosity to particle density ratio just above the critical temperature is $\eta/n|_{T_c}=0.41\pm 0.11$. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above $T_c$ with $\eta/s |_{\it min}=0.50\pm 0.10$.