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

Abstract

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.

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Cited by in corpus (13)

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• Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions
• Analytical results on the magnetization of the Hamiltonian Mean Field model
• Double Lynden-Bell Structure of Low-Energy Quasi-Stationary Distributions in the Hamiltonian Mean-Field Model
• Full Self-Consistent Vlasov-Maxwell Solution