Formation of Multiple Counter-propagating Clusters in the Attractive Hamiltonian Mean-field Model

TL;DR

This paper demonstrates that the attractive Hamiltonian mean-field model can form multiple counter-propagating clusters in phase space, revealing complex quasi-stationary states through particle simulations and a novel wave interaction mechanism.

Contribution

It introduces the existence of multiple cluster states in the Hamiltonian mean-field model and proposes a wave-based mechanism for their formation, expanding understanding of long-range interacting systems.

Findings

Support for stationary states with multiple clusters in phase space

Identification of wave-wave and wave-particle interactions as formation mechanisms

Characterization of these states based on initial simulation parameters

Abstract

Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single non-homogeneous core-halo in the phase-space of the particles. By using particle simulations based on the Hamiltonian mean-field model, we show that this model supports stationary states with multiple cluster or particle holes in phase-space density. We also propose a mechanism based on wave-wave and wave-particle interactions that lead to the formation of these clusters, and characterize these new quasi-stationary states in terms of the initial parameters of the simulations.