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Superstatistical generalised Langevin equation

  • Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellentRecent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.show moreshow less

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Metadaten
Author:Jakub Ślęzak, Ralf MetzlerORCiDGND, Marcin Magdziarz
DOI:https://doi.org/10.1088/1367-2630/aaa3d4
ISSN:(online) 1367-2630
Parent Title (English):New Journal of Physics
Subtitle (English):non-Gaussian viscoelastic anomalous diffusion
Publisher:Deutsche Physikalische Gesellschaft / Institute of Physics
Place of publication:Bad Honnef und London
Document Type:Article
Language:English
Date of first Publication:2018/02/07
Year of Completion:2018
Publishing Institution:Universität Potsdam
Release Date:2018/03/28
Tag:anomalous diffusion; generalised langevin equation; non-Gaussian diffusion; superstatistics
Volume:20
Issue:023026
Pagenumber:25
First Page:1
Last Page:25
Grant Number:PA 2018_03
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publication Way:Open Access
Licence (English):License LogoCreative Commons - Attribution 3.0 unported
Notes extern:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 413