Anomalous diffusion and phase relaxation

The diffusion and relaxation of a phase are investigated on the basis of several stochastic models. A simple relation between the diffusional behavior of the extended phase and the relaxation of periodic phase observables is found in the case of Gaussian and Levy distributed increments. In these cases. an anomalous diffusion gives rise to a stretched exponential relaxation of phase observables. Continuous time random walks may lead, even in the case of normal diffusion, to a slow algebraic relaxation.