Weak ergodicity breaking with deterministic dynamics

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

Received: 26 October 2005
Accepted: 3 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.