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Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

  • We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.

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Author:Andrey G. Cherstvy, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
ISSN:1367-2630 (print)
Parent Title (English):New journal of physics : the open-access journal for physics
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Year of first Publication:2013
Year of Completion:2013
Release Date:2017/03/26
Funder:Academy of Finland (FiDiPro scheme); Deutsche Forschungsgemeinschaft [CH 707/5-1]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Publication Way:Open Access