Issue
Europhys. Lett.
Volume 74, Number 1, April 2006
Page(s) 15 - 21
Section General
DOI http://dx.doi.org/10.1209/epl/i2005-10501-8
Published online 22 February 2006
Europhys. Lett., 74 (1), pp. 15-21 (2006)
DOI: 10.1209/epl/i2005-10501-8

Weak ergodicity breaking with deterministic dynamics

G. Bel and E. Barkai

Physics Department, Bar-Ilan University - Ramat-Gan 52900, Israel


received 26 October 2005; accepted in final form 3 February 2006
published online 22 February 2006

Abstract
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a system whose dynamics is governed by a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase a non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.

PACS
05.45.-a - Nonlinear dynamics and chaos.
05.40.Fb - Random walks and Levy flights.
74.40.+k - Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.).

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