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Ergodic transitions in continuous-time random walks.

Alberto Saa1, Roberto Venegeroles

  • 1Departamento de Matemática Aplicada, UNICAMP, 13083-859 Campinas, SP, Brazil. asaa@ime.unicamp.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study presents a general formula for time-averaged observables in continuous-time random walks. It clarifies transitions between ergodic and nonergodic behaviors, particularly for systems with non-identical trapping times.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Stochastic Processes

Background:

  • Continuous-time random walks (CTRWs) are fundamental models for anomalous transport.
  • Understanding the statistical properties of time-averaged observables in CTRWs is crucial for interpreting experimental data.

Purpose of the Study:

  • To derive a general expression for the distribution of time-averaged observables in CTRWs with arbitrary sojourn time probability density functions.
  • To analyze the conditions leading to ergodic and nonergodic behavior in these systems.

Main Methods:

  • Derivation of a general analytical expression for the distribution of time-averaged observables.
  • Analysis of specific cases, including identically distributed and non-identically distributed sojourn times.
  • Consideration of lattice topology and dimensionality independence.

Main Results:

  • A generalized formula for the distribution of time-averaged observables is obtained.
  • For identically distributed sojourn times, insights into transitions between ergodic and weakly nonergodic regimes are provided.
  • For non-identically distributed trapping times, systems are shown to be typically nonergodic, consistent with blinking quantum dot experiments.

Conclusions:

  • The derived general expression unifies and extends previous results in the literature.
  • The study highlights the prevalence of nonergodicity in CTRWs with heterogeneous waiting times.
  • The findings are applicable across various lattice structures and dimensions.