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

We study hydrodynamic fluctuations in a nonrelativistic fluid. We show that in three dimensions, fluctuations lead to a minimum in the shear viscosity to entropy density ratio n/s as a function of the temperature. The minimum provides a bound n/s which is independent of the conjectured bound in string theory, n/s >= (h) over bar/(4 pi k(B)), where s is the entropy density. For the dilute Fermi gas at unitarity, we find n/s >= 0.2 (h) over bar. This bound is not universal-it depends on the thermodynamic properties of the unitary Fermi gas and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency omega diverges as 1/root omega, and that the shear viscosity in two dimensions diverges as 1n(1/omega). DOI: 10.1103/PhysRevA. 87.023629