Continuous-time random walk approach to on-off diffusion

Statistical properties and scale invariances of on-off diffusion, which is an anomalous transport phenomenon caused by on-off intermittency, are studied on the basis of the continuous-time random walk (CTRW) approach. The anomalous production of heat is also analyzed. Scaling functions of the time evolution of the mean square displacement and the probability density function (PDF) of the position are analytically derived. It is found that there is a characteristic time separating two regimes of time intervals with different scaling laws for the PDF. In the interval that exists at times much smaller than the characteristic time. anomalous subdiffusion appears, which is followed by normal diffusion. In the earlier time interval, aside from the neighborhood of the origin, the PDF takes the form of a power law multiplied by a stretched exponential function. whereas in the later time interval, the PDF becomes a Gaussian. The results are compared with these model simulations. Good agreement between the theory and the simulation is obtained.