Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems

Romain Bachelard (1, 2) , Cristel Chandre (1, 2) , Duccio Fanelli (3) , Xavier Leoncini (1, 2) , Stefano Ruffo (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 Dipartimento di Energetica “Sergio Stecco”

We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian Mean Field model as a case study. We show that an abundance of regular trajectories, associated with invariant tori of the single-particle dynamics, exists. The presence of such tori provides a dynamical interpretation of the emergence of long-lasting out-of-equilibrium regimes observed generically in long-range systems. This is alternative to a previous statistical mechanics approach to such phenomena which was based on a maximum entropy principle. Previously detected out-of-equilibrium phase transitions are also reinterpreted within this framework.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Dynamique Chaotique [nlin.CD]

Romain Bachelard, Cristel Chandre, Duccio Fanelli, Xavier Leoncini, Stefano Ruffo. Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems. 2008. ⟨hal-00322931v1⟩