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

Freddy Bouchet·Thierry Dauxois
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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.

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Freddy Bouchet, Thierry Dauxois. 2005-07-15. Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics. https://doi.org/10.1103/physreve.72.045103

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