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Chaos suppression in the large size limit for long-range systems

M. -C. Firpo·S. Ruffo
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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.

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M. -C. Firpo, S. Ruffo. 2001-08-09. Chaos suppression in the large size limit for long-range systems. https://doi.org/10.1088/0305-4470%2F34%2F37%2F102

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