Chaos suppression in the large size limit for long-range systems
Abstract
We consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the alpha-XY model. This involves N classical rotators on a d-dimensional periodic lattice interacting all to all with an attractive coupling whose strength decays as r^{-alpha}, r being the distances between sites. Using a recent geometrical approach, we estimate for any d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N as a function of alpha in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d between 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These analytical results present a nice agreement with numerical results obtained by Campa et al., including deviations at small N.
Cite
@article{arxiv.cond-mat/0108158,
title = {Chaos suppression in the large size limit for long-range systems},
author = {M. -C. Firpo and S. Ruffo},
journal= {arXiv preprint arXiv:cond-mat/0108158},
year = {2009}
}
Comments
10 pages, 3 eps figures