Apparent fractal dimensions in the HMF model
Statistical Mechanics
2009-11-10 v1
Abstract
We show that recent observations of fractal dimensions in the -space of -body Hamiltonian systems with long-range interactions are due to finite and finite resolution effects. We provide strong numerical evidence that, in the continuum (Vlasov) limit, a set which initially is not a fractal (e.g. a line in 2D) remains such for all finite times. We perform this analysis for the Hamiltonian Mean Field (HMF) model, which describes the motion of a system of fully coupled rotors. The analysis can be indirectly confirmed by studying the evolution of a large set of initial points for the Chirikov standard map.
Cite
@article{arxiv.cond-mat/0407357,
title = {Apparent fractal dimensions in the HMF model},
author = {L. Sguanci and D. H. E. Gross and S. Ruffo},
journal= {arXiv preprint arXiv:cond-mat/0407357},
year = {2009}
}
Comments
Proceedings of the Vlasovia Workshop, Nancy, 26-28 November 2003. to be published on Transport Theory and Statistical Mechanics (Kluwer)