Transport properties for random walks in disordered one-dimensional media: Perturbative calculation around the effective-medium approximation

A perturbation method for the calculation of transport properties in disordered one-dimensional media is presented. It permits considering cases of strong and weak disorder and different initial conditions in a unified way, giving new results and reproducing known ones. The effective-medium approximation (EMA) appears as the zeroth-order step of our diagrammatic scheme. The method is applied to the random-barrier and random-trap models. The range of validity of the EMA is established. Exact results beyond the EMA are obtained for the low-frequency behavior of the frequency-dependent diffusion coefficient and the modified Burnett coefficient associated with the average Green's function and with the response function of the problem.