Ergodicity Breaking in a Deterministic Dynamical System

Details Ergodicity Breaking in a Deterministic Dynamical System Ergodicity Breaking in a Deterministic Dynamical System

2005-07-17

arxiv.org/abs/nlin/0507036v2

Europhys. Lett., 74 (1), pp. 15-21 (2006)

Nonlinear Sciences

Chaotic Dynamics

11 pages, 4 figures

Scientific paper

10.1209/epl/i2005-10501-8

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase 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.

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