Diffusion on finite random media was considered for the case of a time-periodic incoming flow. Particular attention was paid to various boundary conditions (reflecting or absorbing). The situation was analyzed by generalizing the finite effective-medium approximation. A perturbation theory, in the time-asymptotic regime, was therefore formulated in Laplace form for weak and strong site disorder. This separated out, in a natural way, the contributions which arose from the effective medium (due to other higher-order corrections) and appeared in the zeroth-order step of the perturbation scheme. Asymptotic results for the current of probability within the finite domain were obtained for various time-dependent incoming external flows. Exact results were obtained for the low-frequency behavior of the evolution equation of the averaged Green's function on a finite lattice.

Theory of Diffusion in Finite Random Media with a Dynamic Boundary Condition M.O.Cáceres, H.Matsuda, T.Odagaki, D.P.Prato, W.Lamberti: Physical Review B, 1997, 56[10], 5897-908