Nonstationary Markovian replication process causing diverse diffusions.

Abstract

We introduce a single generative mechanism that can be used to describe diverse nonstationary diffusions. A nonstationary Markovian replication process for steps is considered for which we derive analytically the time evolution of the probability distribution of the walker's displacement and the generalized telegrapher equation with time-varying coefficients, and we find that diffusivity can be determined by temporal changes of replication of an immediate step. By controlling the replications, we realize diverse diffusions such as alternating diffusion, superdiffusion, subdiffusion, and marginal diffusion, which originate from oscillating, increasing, decreasing, and slowly increasing or decreasing replications with time, respectively.