A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model

TL;DR

This paper shows that a maximum entropy principle applied to the Vlasov equation explains quasi-stationary states in long-range interacting systems, exemplified by the Hamiltonian Mean Field model, including velocity distributions and new dynamical effects.

Contribution

It introduces a maximum entropy approach to predict quasi-stationary states in the HMF model without adjustable parameters, revealing new dynamical phenomena.

Findings

Velocity distributions match analytical predictions.

Normal diffusion of angles observed.

Discovery of two oscillating clusters with a halo.

Abstract

A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytical expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected and a new dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.