Metastability in the Hamiltonian Mean Field model and Kuramoto model

TL;DR

This paper explores metastable states in the Hamiltonian Mean Field and Kuramoto models, highlighting the role of initial conditions and drawing parallels with glassy dynamics and Tsallis statistics.

Contribution

It presents new findings on metastable states in the Kuramoto model and discusses their similarities with the HMF model, emphasizing metastability as a common feature in coupled systems.

Findings

Metastable states exist in the Kuramoto model.

Initial conditions critically influence metastability.

Metastability may hinder synchronization in coupled systems.

Abstract

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi stationary states observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seem to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering sinchronization.