A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model

TL;DR

This paper investigates the Central Limit Theorem behavior in quasi-stationary states of the Hamiltonian Mean Field model, revealing three distinct classes of states with varying correlations and their dependence on system size.

Contribution

It provides new calculations classifying three types of quasi-stationary states in the HMF model based on their correlation properties and system size dependence.

Findings

Identified three classes of QSS with different correlations

Observed that the occurrence frequency of each class depends on system size

Different microscopic states lead to distinct CLT behaviors

Abstract

We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microsocopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.