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 distance 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 a in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N-kappa, with kappa = 1/3 for 0 less than or equal to alpha /d less than or equal to 1/2 and kappa = 2/3(1 - alpha /d) for 1/2 less than or equal to alpha /d < 1. These analytical results present a nice agreement with numerical results obtained by Campa et al, including deviations at small N.

Chaos suppression in the large size limit for long-range systems / Firpo, M. C.; Ruffo, S.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 34:37(2001), pp. 511-518. [10.1088/0305-4470/34/37/102]

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

Ruffo, S.
2001-01-01

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 distance 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 a in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N-kappa, with kappa = 1/3 for 0 less than or equal to alpha /d less than or equal to 1/2 and kappa = 2/3(1 - alpha /d) for 1/2 less than or equal to alpha /d < 1. These analytical results present a nice agreement with numerical results obtained by Campa et al, including deviations at small N.
2001
34
37
511
518
Firpo, M. C.; Ruffo, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12932
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