Regensburg 2010 – wissenschaftliches Programm

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SYAT: Symposium Anomalous Transport in Heterogeneous Media - from Porous Materials to Cellular Crowding

SYAT 1: Anomalous Transport in Heterogeneous Media I

SYAT 1.1: Hauptvortrag

Mittwoch, 24. März 2010, 14:30–15:00, H1

Aging, ergodicity breaking and universal fluctuations in continuous time random walks: Theory and (possible) experimental manifestations — •Igor Sokolov — Institut für Physik, Humboldt-Universität zu Berlin

We consider some peculiarities of subdiffusive transport within the continuous time random walk (CTRW) model as appearing in the mean-field description of particles’ motion in random potentials (energetic disorder). The anomalous diffusion under CTRW is a process with non-stationary increments. This non-stationarity introduces explicit dependence of observables on the time elapsed from preparing the system in its present state, and corresponds to aging of the process. Aging leads to such unusual properties of the system’s time evolution as death of linear response to an external stimulus or as intrinsic ergodicity breaking. The last can have different manifestations, like the explicit dependence of the moving time averages on the interval of averaging or like universal fluctuations in kinetic coefficients in different realizations of the process. These properties lead to several interesting effects, which are specific for energetic disorder and which can be used for distinguishing this mechanism of anomalous subdiffusion from other possible mechanisms (like the existence of slow modes or diffusion in geometrically disordered systems). We discuss how these properties were (or can be) used in interpretation of experimental or numerical findings, and also consider some cases of anomalous diffusion of mixed origin (e.g. involving geometric and energetic disorder at the same time).