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

Abstract

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 $N\to \infty$, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.

XIV Latin American Workshop on Nonlinear Phenomena (Cartagena, Colombia, Sep. 2015) Keywords : deterministic chaos, stochasticity, mean-field models, propagation of chaos, asymptotic independence, brownian limit, finite N noise, long-range system, hamiltonian dynamics

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions
• Clustering in a model with repulsive long-range interactions
• Phase transitions in simplified models with long-range interactions
• Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures

Cited by in corpus (2)

• Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium
• Contribution of individual degrees of freedom to Lyapunov vectors in many-body systems