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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.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00179877
Contributor : Thierry Dauxois <>
Submitted on : Tuesday, October 16, 2007 - 9:48:18 PM
Last modification on : Tuesday, April 21, 2020 - 10:29:58 AM

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Freddy Bouchet, Thierry Dauxois. Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2005, 72 (4), pp.045103. ⟨ensl-00179877⟩

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