Nonergodicity and central limit behavior for systems with long-range interactions

Details Nonergodicity and central limit behavior for systems with long-range interactions Nonergodicity and central limit behavior for systems with long-range interactions

2007-12-15

arxiv.org/abs/0712.2539v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 figures, paper presented at the International SPIE Conference on Complex Systems, 5-7 December 2007, Canberra, Aust

Scientific paper

10.1117/12.772041

In this paper we discuss the nonergodic behavior for a class of long-standing quasi-stationary states in a paradigmatic model of long-range interacting systems, i.e. the HMF model. We show that ensemble averages and time averages for velocities probability density functions (pdfs) do not coincide and in particular the latter exhibit a tendency to converge towards a q-Gaussian attractor instead of the usual Gaussian one predicted by the Central Limit Theorem, when ergodicity applies.

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