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.
Author details: | Aljaz Godec, Aleksei ChechkinORCiDGND, Eli Barkai, Holger KantzORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8113/47/49/492002 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/26 |
Tag: | Sinai diffusion; anomalous diffusion; quenched energy landscape |
Volume: | 47 |
Issue: | 49 |
Number of pages: | 10 |
Funding institution: | 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 |