Stochastic Ergodicity Breaking: a Random Walk Approach

Details Stochastic Ergodicity Breaking: a Random Walk Approach Stochastic Ergodicity Breaking: a Random Walk Approach

2005-02-05

arxiv.org/abs/cond-mat/0502154v1

Phys. Rev. Lett. 94, 240602 (2005)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.94.240602

The continuous time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann--Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law.

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