Double Lynden-Bell Structure of Low-Energy Quasi-Stationary Distributions in the Hamiltonian Mean-Field Model

TL;DR

This paper investigates the core-halo structure of low-energy quasi-stationary states in the Hamiltonian mean-field model, revealing a superposition of two Lynden-Bell distributions and analyzing their relaxation dynamics.

Contribution

It introduces a double Lynden-Bell structure for low-energy QSS and examines the relaxation process between the two distributions in the Hamiltonian mean-field model.

Findings

Identification of a superposition of two Lynden-Bell distributions in QSS.

Analysis of the relaxation process between the two Lynden-Bell components.

Insights into the completeness of Lynden-Bell relaxation in this context.

Abstract

In the Hamiltonian mean-field model, we study the core-halo structure of low-energy quasi-stationary states under unsteady water-bag type initial conditions. The core-halo structure results in the superposition of two independent Lynden-Bell distributions. We examine the completeness of the Lynden-Bell relaxation and the relaxation between these two Lynden-Bell distributions.