An analysis and extension of the continuous time random walk method. I. Theory

The usual continuous time random walk (CTRW) method for analysing the motion of particles between discrete localised states in disordered systems is fairly simple to apply but involves an averaging procedure whose accuracy is unknown. The Laplace transform of the rate equations for such a system is expressed in matrix form, and it is shown that the usual CTRW approximation corresponds to a certain decoupling of their configurational average. This is the first of a hierarchy of CTRW(n) approximations, which treat exactly transitions involving n steps, and conditions are established for the convergence of this series of approximations.