Lattice gases with static disorder: Renormalization of mean field theory

Abstract

Lattice gas automata are used to model transport phenomena in random media with static disorder. If the interactions are repulsive, there is a large probability of backscattering or retracing collision sequences. In that case the Boltzmann equation or mean field theory breaks down, even in the limit of a low concentration of scatterers. Here sequences of uncorrelated and retracing collisions are of equal importance. The repeated ring approximation is used to resum the retracing trajectories, and the renormalized transport coefficients are calculated in the low-density limit, not only for hard core scatterers (diamonds, hexagons, triangles), but also for mixed point scatterers (mirrors, rotators, reflectors). The results are compared with extensive computer simulations.