Continuous time random walk along inequivalent states

Abstract

A generalisation of the continuous time random walk (CTRW) approach for a system consisting of inequivalent states is presented. The new CTRW equation is found to bear the same structure as that of the CTRW equation for equivalent states, but the parameters have modified forms and meanings. In the earlier approaches the hopping time distribution function was taken to be same for all states, whereas in our generalisation this function is different for different states. Because of the nature of the distribution function, the authors have introduced the probability that the carrier can remain unmoved on a state due to the particular nature of that state. They have generalised the CTRW approach in the situations: (a) where the hopping time distribution is a function of both space and time; and (b) in which the space and time parts of the hopping time distribution function are uncorrelated, i.e. the decoupled case. In the latter situation, the time part of the function is not rigorously space independent in the sense that it depends upon the nature of the state on which the carrier is situated at an instant.