Statistical-mechanical description of diffusion in interacting lattice gases

A Mori-type equation for the lattice concentration of an interacting lattic e gas is constructed on the basis of the master equation in the framework o f the nonequilibrium statistical ensemble method due to Zubarev. The genera l expression for the diffusion coefficient, which takes into account partic le jumps of arbitrary length, spatial dispersion and memory effects is deri ved. in contrast to systems with reversible dynamics the relevant or quasie quilibrium distribution significantly contributes to the diffusion coeffici ent. This contribution is represented by two cofactors. namely the kinetic diffusion coefficient and the correlation function of concentration fluctua tions. For lattice gases with thermally activated hopping dynamics in hydro dynamic (zero frequency and long wave) limit the former is reduced to Zhdan ov's form that reflects an important role of equilibrium characteristics, i .e. the chemical potential and the two-site vacancy distribution function. The self-consistent diagram approximation is used to evaluate these charact eristics for a two-dimensional lattice gas with nearest-neighbor attractive interaction on a square lattice. Results for the diffusion coefficient coi ncide within a few per cent with Monte-Carlo simulation data. (C) 2001 Else vier Science B.V. All rights reserved.