Transition phenomena in diffusive motions due to the change of memory effects

Abstract

In the anomalous diffusions, the transition phenomena from superdiffusion (or subdiffusion) to normal diffusion have been found in several experiments and studied by stochastic models. In this study, we found the diffusion transition which occurs twice in a stochastic process, first from superdiffusion to subdiffusion, and then from subdiffusion to normal diffusion by using the nonstationary Markovian replication process with the memory of the previous step exponentially decaying with time. In the early stage, when the walker strongly follows the previous step, superdiffusive behaviors occur, while in the intermediate stage in which the memory effect decays exponentially, the motion of the walker shows subdiffusive behaviors. Eventually, as the memory effect almost disappears, the motion reduces to normal diffusion. We also found that the Hurst exponent in the intermediate subdiffusive region becomes smaller when the change of the memory effect is more abrupt.