A Simple Model for Long-Range Interacting Pendula
arXiv:1501.04116 · doi:10.1063/1.4980095
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.
References in corpus (6)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
- Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
- Novel Dynamics and Thermodynamics in systems with long range interactions
- Nonlinear Dynamics of Particles Excited by an Electric Curtain
- Computational Studies of Multiple-Particle Nonlinear Dynamics in a Spatio-Temporally periodic potential