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

A. Dechant1,2, E. Lutz1,2, D. A. Kessler3, and E. Barkai3

  • 1Department of Physics, University of Augsburg, 86135 Augsburg, Germany
  • 2Dahlem Center for Complex Quantum Physics, FU Berlin, 14195 Berlin, Germany
  • 3Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel

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Phys. Rev. E 85, 051124 – Published 16 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.051124

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.

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Phys. Rev. E 85, 051124– Published 16 May, 2012
  • Received 1 March 2012

©2012 American Physical Society

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