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  Localisation and universal fluctuations in ultraslow diffusion processes.

Godec, A., Chechkin, A. V., Barkai, E., Kantz, H., & Metzler, R. (2014). Localisation and universal fluctuations in ultraslow diffusion processes. Journal of Physics A: Mathematical and Theoretical, 47(49): 492002. doi:10.1088/1751-8113/47/49/492002.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-CB6F-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-CB72-4
Genre: Journal Article

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Godec, A.1, Author              
Chechkin, A. V., Author
Barkai, E., Author
Kantz, H., Author
Metzler, R., Author
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1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              

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Free keywords: Sinai diffusion; anomalous diffusion; quenched energy landscape
 Abstract: 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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Language(s): eng - English
 Dates: 2014-11-14
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1751-8113/47/49/492002
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Title: Journal of Physics A: Mathematical and Theoretical
Source Genre: Journal
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Pages: 10 Volume / Issue: 47 (49) Sequence Number: 492002 Start / End Page: - Identifier: -