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… 
View on IOP Publishing
arxiv.org
3 Citations
Background Citations
2

3 Citations

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

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

Ergodicity and slow relaxation in the one-dimensional self-gravitating system

References

SHOWING 1-10 OF 23 REFERENCES

Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures.

  • W. EttoumiM. Firpo
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence toward equilibrium of mean-field systems due to finite-N effects. The…

Clustering and relaxation in Hamiltonian long-range dynamics.

  • AntoniRuffo
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
A two-cluster drifting state with zero magnetization forms spontaneously at very small temperatures; at larger temperatures an initial density modulation produces this state, which relaxes very slowly, which suggests the possibility of exciting magnetized states in a mean-field antiferromagnetic system.

The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back

The thermodynamics and the dynamics of particle systems with infiniterange coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian…

Nonequilibrium phase transitions and violent relaxation in the Hamiltonian mean-field model.

The nature of nonequilibrium phase transitions in the Hamiltonian mean-field model using detailed numerical simulations of the Vlasov equation and molecular dynamics shows that the phase transitions are either first order or are composed of a cascade of phase reentrances.

Gaussian Convergence for Stochastic Acceleration of Particles in the Dense Spectrum Limit

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where…

Ergodicity breaking and parametric resonances in systems with long-range interactions.

It is shown that if the initial distribution satisfies a specific constraint-a generalized virial condition-the quasistationary state is very close to ergodic and can be described by Lynden-Bell statistics, on the other hand, if the generalized virials condition is violated, parametric resonances are excited, leading to chaos and ergodicity breaking.

Large Scale Dynamics of Interacting Particles

Scales.- Outline.- I Classical Particles.- 1. Dynamics.- 1.1 Newtonian Dynamics.- 1.2 Boundary Conditions.- 1.3 Dynamics of Infinitely Many Particles.- 2. States of Equilibrium and Local…

Phase transitions in simplified models with long-range interactions.

A behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies.

Dynamics and thermodynamics of systems with long-range interactions

Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction.- Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction.- Statistical Mechanics.-…

Long-range interacting systems : École d'été de physique des Houches, session XC, 4-29 August, 2008 : École thématique du CNRS

PART I: STATISTICAL DYNAMICS 1. Statistical Mechanics of Systems with Long-Range Interactions 2. Six out of equilibrium lectures 3. Synchronization of regular and chaotic oscillators PART II:…