Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

A. Dechant, E. Lutz, D. A. Kessler, E. Barkai

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Original languageEnglish
Article number051124
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume85
Issue number5
DOIs
Publication statusPublished - 2012 May 16
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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