Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

Andrey G. Cherstvy, Aleksei V. Chechkin, 3 and Ralf Metzler 4 Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany Department of Physics, Tampere Univ...

Self-averaging and ergodicity of subdiffusion in quenched random media.

We study the self-averaging properties and ergodicity of the mean square displacement m(t) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m(t). We find that m(t) is not self-averaging for d<2 due to the inefficient d...

In vivo anomalous diffusion and weak ergodicity breaking of lipid granules.

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads ...

Weak ergodicity breaking in an anomalous diffusion process of mixed origins.

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report, this parameter is calculated for fractional Brownian motion with a random change of time scale, often called "subordination." We show that this quantity is the same as the known continuous time random walks case.

Weak-ergodicity Breaking in Mean-field Spin-glass Models