Nonlinear Transport Phenomena: Analysis in Terms of Density Expansions

A microscopic calculation of the long-time tail in the autocorrelation function corresponding to the mutual diffusion coefficient is presented. Mode-coupling methods in the framework of a generalized Langevin equation are used to obtain the results. The calculation yields an expression for the mutual diffusion coefficient in terms of two quantities; a bare mutual diffusion coefficient $D^{*}$ and a complicated nonlinear transport coefficient $\alpha$. Density expansions of these transport coefficients are carried out in order to elucidate their structure. In particular, we investigate, for dense gases, the conditions under which $\alpha$ reduces to a factored form involving the kinematic viscosity and diffusion coefficient, and the relation between $D^{*}$ and the usual mutual diffusion coefficient.