Particle Tracking and NanotechnologyOpen Access

Weak ergodicity breaking and ageing in anomalous diffusion

Ralf Metzler

Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany

Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland

https://doi.org/10.1142/S2010194515600071Cited by:9 (Source: Crossref)

Abstract

Modern single particle tracking techniques and many large scale simulations produce time series r(t) of the position of a tracer particle. Standardly these are evaluated in terms of the time averaged mean squared displacement. For ergodic processes such as Brownian motion, one can interpret the results of such an analysis in terms of the known theories for the corresponding ensemble averaged mean squared displacement, if only the measurement time is sufficiently long. In anomalous diffusion processes, that are widely observed over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking). In such cases the time averages may no longer be interpreted in terms of ensemble theories. Here we collect some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement and the inherent irreproducibility of individual measurements. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 3.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

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Published: 2 January 2015

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Weak ergodicity breaking and ageing in anomalous diffusion

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