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

摘要

Using the continuous-time random walk (CTRW) approach, we study thephenomenon of relaxation of two-state systems whose elements evolve accordingto a dichotomous process. Two characteristics of relaxation, the probabilitydensity function of the waiting times difference and the relaxation law, are ofour particular interest. For systems characterized by Erlang distributions ofwaiting times, we consider different regimes of relaxation and show that, undercertain conditions, the relaxation process can be non-monotonic. By studyingthe asymptotic behavior of the relaxation process, we demonstrate that heavyand superheavy tails of waiting time distributions correspond to slow andsuperslow relaxation, respectively.