Stochastic transport in disordered systems

Abstract

We develop a theory of stochastic transport in disordered media, starting from a linear master equation with random transition rates. A Green function formalism is employed to reduce the basic equation to a form suitable for the construction of a class of effective medium approximations (EMAs). The lowest order EMA, developed in detail here, corresponds to recent approximations proposed by Odagaki and Lax [Phys. Rev. B 24, 5284 (1981], Summerfield [Solid State Commun. 39, 401 (1981)], and Webman [Phys. Rev. Lett. 47, 1496 (1981)]. It yields an effective transition rate Wm which can be identified as the memory kernel of a generalized master equation, and used to define an associated continuou..