Monitoring Levy-process crossovers

The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different Levy processes: in the first model we change gradually the order of the derivative in the Laplacian term of the diffusion equation, whereas in the second one we consider a combination of fractional-derivative diffusive terms characterized by coefficients that change in time. The proposals are illustrated by considering semi-analytical (i.e., analytical together with numerical) procedures to follow the time-dependent solutions. We find changes between two different regimes and it is shown that, far from the crossover regime, both models yield qualitatively similar results, although these changes may occur in different forms for the two models. The models introduced herein are expected to be useful for describing crossovers among distinct diffusive regimes that occur frequently in complex systems. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The crossover between different Levy processes is an important theme in nonequilibrium statistical physics. Two models are proposed in this work to generate crossovers, demonstrating qualitatively similar results far from the crossover regime. These models are expected to be useful for describing crossovers among distinct diffusive regimes in complex systems.