Abundance of regular orbits and nonequilibrium phase transitions in the thermodynamic limit for long-range systems.
We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian mean-field model as a case study. We show that regular trajectories, associated with invariant tori of the single-particle dynamics, prevail. 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.
Bachelard
R
R
Centre de Physique Théorique, CNRS--Aix-Marseille Université, Luminy, Case 907, F-13288 Marseille cedex 9, France.
Chandre
C
C
Fanelli
D
D
Leoncini
X
X
Ruffo
S
S