Diffusion in lattice Lorentz gases with a percolation threshold

A mean-field approximation for the diffusion coefficient in lattice Lorentz gases with an arbitrary mixture of pointlike stochastic scatterers in the low-density limit is proposed. In this approximation, the diffusion coeffic ient is directly related to the first return probability of the moving part icle in the corresponding Cayley tree through an effective ring operator. A renormalization scheme for the approximate determination of the first retu rn probability is constructed. The predictions of this mean-field theory an d those of the repeated ring approximation (RRA) are compared with computer simulation results for models in which a fraction x(B) of the scatterers a re deterministic backscatterers, so that the diffusion coefficient vanishes beyond a certain percolation threshold x(B)(c),. The approximation propose d in this paper is seen to be in good agreement with the simulation results , in contrast to the RRA, which already fails to give the correct percolati on threshold. [S1063-651X(99)10807-9].