Quasi-stationary trajectories of the HMF model: a topological perspective

TL;DR

This paper uses a topological approach to study quasi-stationary states in the HMF model, revealing that the system evolves along a manifold of critical points with marginal stability, explaining slow relaxation.

Contribution

It introduces a topological perspective to analyze the quasi-stationary states of the HMF model, combining numerical and analytical methods.

Findings

System evolves along a manifold of critical points.

Critical points are maxima with many marginal directions.

Explains slow relaxation and trapping in quasi-stationary states.

Abstract

We employ a topological approach to investigate the nature of quasi-stationary states of the Mean Field XY Hamiltonian model that arise when the system is initially prepared in a fully magnetized configuration. By means of numerical simulations and analytical considerations, we show that, along the quasi-stationary trajectories, the system evolves in a manifold of critical points of the potential energy function. Although these critical points are maxima, the large number of directions with marginal stability may be responsible for the slow relaxation dynamics and the trapping of the system in such trajectories.