Low-Frequency Behavior of Transport Coefficients in Fluids

It was recently shown that the kinetic-kinetic part of the Kubo integrands for shear viscosity and heat conductivity behaves as t^-d/2(d=dimensionality) for t→∞. 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→∞. The method is very similar to that used in the Landau-Placzeck calculation of the light-scattering cross section of simple fluids. This t^-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.