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Localisation and universal fluctuations in ultraslow diffusion processes

  • We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.

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Author:Aljaz Godec, Aleksei V. ChechkinORCiDGND, Eli Barkai, Holger Kantz, Ralf MetzlerORCiDGND
ISSN:1751-8113 (print)
ISSN:1751-8121 (online)
Parent Title (English):Journal of physics : A, Mathematical and theoretical
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/26
Tag:Sinai diffusion; anomalous diffusion; quenched energy landscape
Funder:Academy of Finland (FiDiPro scheme); Alexander von Humboldt Foundation; Berlin Mathematical Society; Israel Science Foundation
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert