Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

Understand

We study hydrodynamic fluctuations in a non-relativistic fluid.

• We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature.
• The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density.
• For the dilute Fermi gas at unitarity we find $\eta/s\gsim 0.2\hbar$.