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

TL;DR

This paper studies long-range interacting systems, revealing many regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit, offering a dynamical perspective distinct from traditional statistical mechanics.

Contribution

It demonstrates the prevalence of regular trajectories and reinterprets out-of-equilibrium phase transitions through a dynamical lens in long-range systems.

Findings

Abundance of regular trajectories linked to invariant tori.

Long-lasting out-of-equilibrium regimes are explained dynamically.

Reinterpretation of out-of-equilibrium phase transitions.

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.