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Article Dans Une Revue Physica Scripta Année : 2016

Brownian regime of finite- N corrections to particle motion in the XY Hamiltonian mean field model

Résumé

We study the dynamics of the N-particle system evolving in the XY hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent brownian noises over a time scale diverging not slower than N^(2/5) as N → ∞, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
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Dates et versions

hal-01316408 , version 1 (17-05-2016)

Identifiants

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Bruno V Ribeiro, Marco A Amato, Yves Elskens. Brownian regime of finite- N corrections to particle motion in the XY Hamiltonian mean field model. Physica Scripta, 2016, Focus issue on the XIV Latin American Workshop on Nonlinear Phenomena, 91 (8), pp.084004. ⟨10.1088/0031-8949/91/8/084004⟩. ⟨hal-01316408⟩

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