Microscopic approach to the collective diffusion in the interacting lattice gas

A variational approach to collective diffusion in the interacting lattice gas, based on kinetics of microscopic states of the system, is presented. The approach accounts for equilibrium correlations and is capable of predicting the coverage dependence of the diffusion coefficient D(θ) in an analytic form. It provides a viable alternative to approaches based on a hierarchy of kinetic equations for correlation functions and in contrast to them is free of uncertainties often introduced by various truncation schemes. Applications to one-dimensional lattice gas models with increasing degree of complexity are presented. A two-dimensional gas with strong interparticle repulsive interactions is chosen to illustrate the application to a system with structural ordering. In each case, analytic predictions agree very well with the results of the Monte Carlo simulations. In particular, rapid changes/discontinuities of D(θ), discovered in numerical simulations, are confirmed and their origin understood.