Nonlinear effects in diffusion processes

Several aspects of the mode-coupling description of the long-time behavior of the autocorrelation function corresponding to the mutual- and self-diffusion coefficients are investigated. Our calculations of the generalized diffusion coefficient are carried out by employing a set of linear, bilinear, and trilinear variables in the generalized Langevin equation. The diffusion coefficient is expressed in terms of a bare diffusion coefficient and a frequency- and wave-number-dependent nonlinear transport coefficient, which in turn can be written as a bare nonlinear transport coefficient plus a frequency- and wave-number-dependent term. We discuss the validity of calculations that take into account only bilinear coupling. For the case of test-particle diffusion, we examine the structure of the transport coefficients that enter in the mode-coupling calculation by making use of the techniques in the density expansions of transport coefficients. By summing a certain class of collisions to all orders in the density, we show how that part of the bare diffusion coefficient which corresponds to a cross correlation between the test-particle momentum and that of the bath exactly cancels that part of the velocity-autocorrelation function that gives rise to the long-time tail. The bare nonlinear transport coefficient is also examined.