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

Abstract

We consider the class of long-range Hamiltonian systems first introduced by\nAnteneodo and Tsallis and called the alpha-XY model. This involves N classical\nrotators on a d-dimensional periodic lattice interacting all to all with an\nattractive coupling whose strength decays as r^{-alpha}, r being the distances\nbetween sites. Using a recent geometrical approach, we estimate for any\nd-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N\nas a function of alpha in the large energy regime where rotators behave almost\nfreely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d\nbetween 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These\nanalytical results present a nice agreement with numerical results obtained by\nCampa et al., including deviations at small N.\n