Statistical model for stretched exponential relaxation in macroscopic systems

We develop a statistical model for the stretched exponential relaxation, exp[-(t/τ${)}^{\alpha }$], observed in many macroscopic systems. The model, which is suggested by theories for the decay of luminescence in the presence of a random distribution of traps, is applicable in two cases. The macroscopic system is composed of a number of similar, weakly interacting subsystems all of which are characterized by the same set of relaxation channels and rates, with the subsystems differing from one another in the channels which are blocked. Alternatively, the model is appropriate to a situation where the relaxation channels open and close randomly in time with the correlation times for the fluctuations being long in comparison with the reciprocals of the corresponding rates. The parameter α characterizing the relaxation is related to the limiting behavior of a weighted density of relaxation rates. As a special case, the model reproduces results obtained previously for luminescence decay at low trap concentration.