A Simple Model for Long-Range Interacting Pendula
Classical Physics
2018-09-06 v2
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.
Cite
@article{arxiv.1501.04116,
title = {A Simple Model for Long-Range Interacting Pendula},
author = {Owen Myers and Adrian Del Maestro and Junru Wu and Jeffrey S. Marshall},
journal= {arXiv preprint arXiv:1501.04116},
year = {2018}
}