Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes
- Institute for Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Tampere University of Technology, FI-33101 Tampere (Finland)
Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. 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.
- OSTI ID:
- 22264078
- Journal Information:
- AIP Conference Proceedings, Vol. 1579, Issue 1; Conference: 5. Leopoldo Garcia-Colin Mexican meeting on mathematical and experimental physics, Mexico City (Mexico), 9-13 Sep 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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