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We study the dynamics of the N-particle system evolving in the XY hamiltonianmean field (HMF) model for a repulsive potential, when no phase transitionoccurs. Starting from a homogeneous distribution, particles evolve in a meanfield created by the interaction with all others. This interaction does notchange the homogeneous state of the system, and particle motion isapproximately ballistic with small corrections. For initial particle dataapproaching a waterbag, it is explicitly proved that corrections to theballistic velocities are in the form of independent brownian noises over a timescale diverging not slower than $N^{2/5}$ as $N \to \infty$, which proves thepropagation of molecular chaos. Molecular dynamics simulations of the XY-HMFmodel confirm our analytical findings.

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