Logarithmic Term in the Density Expansion of Transport Coefficients

Abstract

A divergence in the first (second) density correction to the transport coefficients of two- (three-) dimensional classical gases has been studied using the resolvent-operator formalism of the correlation-function expressions for the transport coefficients. As an illustration we consider the self-diffusion coefficient of the two-dimensional gas. A divergence in the triple-collision term arises from the behavior of the integrand at small values of the wave vector in the integration over the wave vector. Similar and stronger divergences appear in higher terms of the binary-collision expansion. The most divergent terms have been summed with the help of a diagram analysis and are shown to provide a natural cutoff to the divergence in the triple-collision term. The cutoff wave vector is proportional to the density $\ensuremath{\rho}$ and gives rise to a term involving $\mathrm{ln}\ensuremath{\rho}$ in the density correction to the transport coefficients.