A Simple Model for Long-Range Interacting Pendula

TL;DR

This paper demonstrates that the Hamiltonian mean field model effectively describes the equilibrium and non-equilibrium behaviors of long-range interacting pendula systems, revealing novel clustering phenomena.

Contribution

It introduces a new application of the HMF model to long-range coupled pendula and analyzes both equilibrium and non-equilibrium dynamics with a focus on clustering behavior.

Findings

HMF model describes equilibrium of long-range pendula systems.

Existence of quasistationary clustered states in non-equilibrium.

Inclusion of index-dependent phase in the interaction term.

Abstract

We show that the Hamiltonian mean field (HMF) model describes the equilibrium behavior of a system of long pendula with flat bobs that are coupled through long-range interactions (charged or self gravitating). We solve for the canonical partition function in the coordinate frame of the pendula angles. The Hamiltonian in the angles coordinate frame looks similar to the form of the HMF model but with the inclusion of an index dependent phase in the interaction term. We also show interesting non-equilibrium behavior of the pendula angles, namely that a quasistationary clustered state can exist when pendula angles are initially ordered by their index.