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

Freddy Bouchet 1 Thierry Dauxois 1
1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
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.
Keywords : HMF model statistical mechanics
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Journal articles
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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 : Wednesday, November 20, 2019 - 2:47:58 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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