GENERALIZED EFFECTIVE-MEDIUM APPROXIMATION FOR PARTICLE-TRANSPORT - RANDOM-TRAP MODEL

The effective-medium approximation for particle transport on lattices with random traps is generalized to include weighted initial conditions. It is argued that an inhomogeneous term must be included in the generalized master equation. We provide results for d-dimensional lattices with random traps and uniform bias fields. The effective-medium-approximation results in one and two dimensions are compared with numerical simulations for selected moments up to fourth order, and for the conditional probability distribution. Good agreement between theory and simulation is found; this confirms the necessity of including an inhomogeneous term and provides an accurate procedure for other models of transport in disordered media.