2020/09/13 by M. A. F. dos Santos, Santos, Maike A. F. dos, Fernando Nobre +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2009.06015
openalex publication_date 2020/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Lévy 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.