Anomalous diffusion and quasistationarity in the HMF model

TL;DR

This paper investigates the quasistationary states of the Hamiltonian Mean Field Model, revealing multiple diffusive behaviors and emphasizing the importance of finite size effects and careful averaging in non-ergodic regimes.

Contribution

It identifies three classes of diffusive events in the HMF model's quasistationary regime and highlights the impact of finite size effects on system behavior.

Findings

Existence of three diffusive event classes

Finite size effects significantly influence diffusive properties

Caution needed when replacing time averages with ensemble averages

Abstract

We explore the quasistationary regime of the Hamiltonian Mean Field Model (HMF) showing that at least three different classes of events exist, with a different diffusive behavior and with a relative frequency which depends on the size of the system. Along the same line of a recent work \cite{epl}, these results indicate that one must be very careful in exchanging time averages with ensemble averages during the non-ergodic metastable regime and at the same time they emphasize the role of finite size effects in the evaluation of the diffusive properties of the system.