Volume 74, Number 1, April 2006
|Page(s)||15 - 21|
|Published online||22 February 2006|
Weak ergodicity breaking with deterministic dynamics
Physics Department, Bar-Ilan University - Ramat-Gan 52900, Israel
Accepted: 3 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.
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.)
© EDP Sciences, 2006
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