Long time dynamics close to a percolation threshold

The response function for random walks on a bond disordered lattice is calculated in the effective medium approximation (EMA). The basis for this approximation is reviewed and several exact limits preserved by this model are noted. For low density bond disorder the velocity autocorrelation function is calculated from the EMA and compared with exact expansions to order c2. More generally, the long time dynamics is shown to have a universal form over a wide range of densities. However, at densities close to the percolation threshold this form is modified. In particular, the amplitudes of the long time tails are found to be divergent at the threshold, indicating a crossover to a qualitatively different dynamics. This crossover phenomenon is investigated analytically and numerically for the EMA.