Phase Diagram in Stored-Energy-Driven L\'evy Flight

TL;DR

This paper presents a phase diagram for the stored-energy-driven Lévy flight, revealing diverse anomalous diffusion behaviors and the intrinsic distributional properties of time-averaged MSD across different regimes.

Contribution

It analytically derives the phase diagram of SEDLF based on coupling parameters and trapping-time distribution, highlighting intrinsic distributional behaviors.

Findings

Identifies regimes of subdiffusion, normal diffusion, and superdiffusion.

Shows distributional behavior of time-averaged MSD in superdiffusive and normal regimes.

Provides analytical phase diagram using renewal theory.

Abstract

Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven L\'evy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move while storing energy, and it jumps by the stored energy. The SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion, depending on the coupling parameter between storing time (trapping time) and stored energy. This stochastic process can be investigated analytically with the aid of renewal theory. Here, we consider two different renewal processes, i.e., ordinary renewal process and equilibrium renewal process, when the mean trapping time does not diverge. We analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping-time distribution. In particular, we find that distributional behavior of time-averaged MSD intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge.