Effective-medium approximation with asymmetric transition rates

An effective-medium approximation considering asymmetric transition rates is presented for a D-dimensional anisotropic random walk. Our approach allows to obtain a set of $2D$ frequency-dependent effective transition rates in a self-consistent way. Even when these coupled equations could look unwielding, we have been able to work out some particular cases, i.e., using a separablelike ansatz the asymmetric effective-medium approximation is shown to be reduced, under a transformation of variables, to the study of the symmetric case. Within this basic formalism, a biased diffusion problem in an anisotropic two-dimensional percolation model is analyzed. The asymmetric effective-medium approximation is finally compared against Monte Carlo simulations, and a good agreement is found for small bias values.