Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities

  • A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.

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Metadaten
Author:Aleksei V. Chechkin, Flavio Seno, Ralf MetzlerORCiD, Igor M. Sokolov
DOI:https://doi.org/10.1103/PhysRevX.7.021002
ISSN:2160-3308
Parent Title (English):Physical review : X, Expanding access
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Language:English
Year of first Publication:2017
Year of Completion:2017
Release Date:2020/04/20
Volume:7
Pagenumber:20
Funder:Deutsche Forschungsgemeinschaft; Deutscher Akademischer Austauschdienst (DAAD)
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert