Europhys. Lett.
Volume 74, Number 1, April 2006
Page(s) 15 - 21
Section General
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

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.

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.).

© EDP Sciences 2006