Dynamic percolation and diffusion in disordered systems

Abstract

The author has studied diffusion in a disordered network in which the transition rates of the bonds of the network are dependent on time. He solves the problem by making an effective-medium approximation (EMA) and find that if the values of the transition rates vary between two values with a relaxation time t_R, and if W_m( lambda ) is the Laplace-transformed solution of the problem in the limit t_R= infinity , then W_m( lambda +t_R^-1) is the solution of the dynamic problem for any value of t_R. The EMA also predicts that the percolation threshold of the system is zero if t_R not=0. Some applications of this problem are also discussed.