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

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.