Ergodic transitions in continuous-time random walks

Abstract

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes. On the other hand, for the case of non-identical trapping time densities over the lattice points, the distribution of time-averaged observables reveals that such systems are typically nonergodic, in agreement with some recent experimental evidences on the statistics of blinking quantum dots. Some explicit examples are considered in detail. Our results are independent of the lattice topology and dimensionality.

8 pages, final version to appear in PRE

References in corpus (6)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Weakly non-ergodic Statistical Physics
• Ergodicity Breaking in a Deterministic Dynamical System
• A Random Walk to a Non-Ergodic Equilibrium Concept