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

Abstract

A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably the disintegration of coherent structures that may sustain out-of-equilibrium quasistationary states. The time evolution of the fraction of particles remaining close to a mean-field potential trough is analytically computed. This indicator enables to estimate the lifetime of coherent structures and thermalization timescale in mean-field systems.

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Slow relaxation in long-range interacting systems with stochastic dynamics
• Quasi-stationary states and the range of pair interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Linear theory and violent relaxation in long-range systems: a test case

Cited by in corpus (4)

• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
• Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
• Contribution of individual degrees of freedom to Lyapunov vectors in many-body systems