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

@article{Ribeiro2016BrownianRO, title={Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model}, author={Bruno V. Ribeiro and Marco Ant{\^o}nio Amato and Yves Elskens}, journal={Physica Scripta}, year={2016}, volume={91} }

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…

## 3 Citations

### Strange scaling and relaxation of finite-size fluctuation in thermal equilibrium.

- PhysicsPhysical review. E
- 2016

A scenario is proposed to explain two strange phenomena of finite-size fluctuation in thermal equilibrium of a paradigmatic long-range interacting system having a second-order phase transition from the viewpoint of the Casimir invariants and their nonexactness in finite- size systems, where the Cas Vladimir invariants are conserved in the Vlasov dynamics describing the long- range interacting systems in the limit of large population.

### Contribution of individual degrees of freedom to Lyapunov vectors in many-body systems

- PhysicsCommun. Nonlinear Sci. Numer. Simul.
- 2019

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