Crossover dynamics in bond disordered lattices

Abstract

The asymptotic dynamics of the percolation model for a bond disordered lattice is studied. The velocity autocorrelation function (VACF) is investigated for arbitrary concentration of disorder in two and three dimensions using an effective medium approximation (EMA). Corrections to the long time tails away from the percolation threshold and to the percolation tails at the threshold are calculated. A characteristic time scale for the long time tails is identified and found to diverge at the threshold. Sufficiently close to the threshold the two types of asymptotic dynamics can be identified clearly for times greater than and less than this characteristic time, respectively. An approximate scaling of the EMA equation is obtained near the threshold for investigation of the crossover region. More generally, the EMA equation is solved numerically for arbitrary concentration in two dimensions to exhibit the complete time dependence of the VACF in all domains near and far from the threshold.