Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics.
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.
Bouchet
Freddy
F
Laboratoire de Physique, UMR CNRS 5672, Ecole Normale Supérieurs de Lyon, 46, allée d'Italie, 69007 Lyon, France.
Dauxois
Thierry
T