Weak Chaos in large conservative system -- Infinite-range coupled standard maps

TL;DR

This paper investigates a globally coupled map system that bridges discrete nonlinear dynamics and long-range Hamiltonian models, revealing long-lasting quasistationary states and weak chaos in the thermodynamic limit, similar to the Hamiltonian Mean Field model.

Contribution

It introduces a new perspective on coupled map systems, demonstrating their connection to long-range Hamiltonian models and their shared dynamical features.

Findings

Existence of long-lasting quasistationary states (QSS).

Emergence of weak chaos in the thermodynamic limit.

Reveals similarities with the Hamiltonian Mean Field model.

Abstract

We study, through a new perspective, a globally coupled map system that essentially interpolates between simple discrete-time nonlinear dynamics and certain long-range many-body Hamiltonian models. In particular, we exhibit relevant similarities, namely (i) the existence of long-standing quasistationary states (QSS), and (ii) the emergence of weak chaos in the thermodynamic limit, between the present model and the Hamiltonian Mean Field model, a strong candidate for a nonxtensive statistical mechanical approach.