Coupled continuous time random walk with Lévy distribution jump length signifies anomalous diffusion?

Abstract

The continuous time random walk (CTRW) models are highly valued for studying anomalous diffusion, a ubiquitous phenomenon in complex media whose mean squared displacement (MSD) exhibits power-law behavior. It is widely accepted that the Lévy distribution jump length of random particles with infinite second moment could be responsible for the superdiffusion phenomenon. In this paper, we study the coupled CTRW with exponentially truncated Lévy distribution jump length, deduce the corresponding integrodifferential diffusion equation, and give the propagator expression. It is interesting that we find the MSD for random particles is linearly related to time in the symmetric Lévy distribution case, and it reduces to a simple expression. Additionally, for a non-zero truncated exponent, the MSD also has a linear relationship with time, which reflects the special dependence between waiting time and jump length in this coupled CTRW model.