Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model

TL;DR

This paper reviews the core-halo structure of quasi-stationary states in the Hamiltonian mean-field model, showing it can be described by a superposition of two Lynden-Bell distributions and discussing their relaxation properties.

Contribution

It provides a comprehensive analysis of the core-halo structure in QSSs, introducing a double Lynden-Bell distribution framework for the Hamiltonian mean-field model.

Findings

Core-halo structure described by superposition of two Lynden-Bell distributions.

Double Lynden-Bell distribution effectively models QSSs.

Collisionless relaxation analyzed using Lynden-Bell entropies.

Abstract

A characteristic feature of long-range interacting systems is that they become trapped in a non-equilibrium and long-lived quasi-stationary state (QSS) during the early stages of their development. We present a comprehensive review of recent studies of the core-halo structure of QSSs, in the Hamiltonian mean-field model, which is a mean-field model of mutually coupled ferromagnetic XY spins located at a point, obtained by starting from various unsteady rectangular water-bag type initial phase-space distributions. The main result exposed in this review is that the core-halo structure can be described by the superposition of two independent Lynden-Bell distributions. We discuss the completeness of collisionless relaxation of this double Lynden-Bell distribution by using both of Lynden-Bell entropy and double Lynden-Bell entropy for the systems at low energies per particle.