Relaxation Processes and Time Scale Transformation.

Abstract : Stochastic processes with a special class of non-stationary transition rates (NSTR) that can be related to stationary rates (STR) by time scale transformations are considered. Calculations are carried out on the time scale on which the process has STR and then related to the time scale of measurements by a time scale transformation. Application is made to Gaussian Markoff processes with a single transition rate. The resulting equilibrium autocorrelation function departs from weak stationarity. A response function is related to the Autocorrelation function and specialized to relaxation processes to yield a model consistent with Ngai's recent model of relaxation. The model is therefore widely applicable in the description of measured relaxation behavior and leads naturally to Ngai's renormalization relation for excitation energies. On the basis of the success of the model, consideration is given to the possibility that the process should be viewed as one with STR and an intrinsic time scale so that the process only appears to have NSTR on the time scale of measurements. (Author)