Continuous-time random walk model of relaxation of two-state systems

Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function of the waiting times difference and the relaxation law, are of our particular interest. For systems characterized by Erlang distributions of waiting times, we consider different regimes of relaxation and show that, under certain conditions, the relaxation process can be non-monotonic. By studying the asymptotic behavior of the relaxation process, we demonstrate that heavy and superheavy tails of waiting time distributions correspond to slow and superslow relaxation, respectively.