Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics

TL;DR

This paper uses classical kinetic theory to explain slow, non-Gaussian out-of-equilibrium behaviors and anomalous diffusion in long-range interacting systems, specifically the Hamiltonian Mean-Field model.

Contribution

It derives a Fokker-Planck equation for a test particle that predicts slow relaxation and anomalous diffusion without resorting to Non-Extensive Statistical Mechanics.

Findings

Predicts algebraic relaxation of momentum autocorrelation

Explains non-Gaussian out-of-equilibrium distributions

Forecasts angular anomalous diffusion for various initial conditions

Abstract

We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one also unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation, previously found in numerical simulations. Finally, angular anomalous diffusion are predicted for a large class of initial distributions. Non Extensive Statistical Mechanics is shown to be unnecessary for the interpretation of these phenomena.