Details

Autor(en) / Beteiligte

• Miranda Filho, L H
• Amato, M A
• Rocha Filho, T M

Titel

Lyapunov exponent and criticality in the Hamiltonian mean field model

Ist Teil von

• Journal of statistical mechanics, 2018-03, Vol.2018 (3), p.33204

Ort / Verlag

IOP Publishing and SISSA

Erscheinungsjahr

2018

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.