Non-stationary Markovian Replication Process causing Diverse Diffusions

TL;DR

This paper presents a non-stationary Markovian replication process that models various types of diffusion by controlling step replications, providing analytical solutions for the probability distribution and diffusion behaviors.

Contribution

It introduces a unified mechanism to describe diverse non-stationary diffusions through a Markovian process with analytically derived dynamics.

Findings

Derived time-evolution of displacement distribution

Established connection between replication control and diffusion type

Demonstrated ability to model various diffusion regimes

Abstract

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