Clifford Chafin, Thomas Schaefer
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 density ratio $\eta/n$ as a function of the temperature. The minimum provides a bound on $\eta/n$ 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 $\eta/n\gsim 0.3\hbar$. This bound is not rigorous, but it can only be avoided if the domain of validity of hydrodynamics is anomalously small. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.
View original:
http://arxiv.org/abs/1209.1006
No comments:
Post a Comment