Low-Frequency Behavior of Transport Coefficients in Fluids

Abstract

It was recently shown that the kinetic-kinetic part of the Kubo integrands for shear viscosity and heat conductivity behaves as ${t}^{\ensuremath{-}\frac{d}{2}}(d=\mathrm{dimensionality})$ for $t\ensuremath{\rightarrow}\ensuremath{\infty}$. We generalize this result to the complete (kinetic-kinetic + kinetic-potential + potential-potential) Kubo integrands for bulk and shear viscosity and heat conductivity and find explicitly the leading-order term for these autocorrelation functions for $t\ensuremath{\rightarrow}\ensuremath{\infty}$. The method is very similar to that used in the Landau-Placzeck calculation of the light-scattering cross section of simple fluids. This ${t}^{\ensuremath{-}\frac{d}{2}}$ behavior has two consequences that are examined: In two-dimensional fluids it leads to a divergence of Kubo integrals and in three dimensions it yields a nonanalytical low-frequency behavior of the frequency-dependent transport coefficients.