On the effectiveness of mixing in violent relaxation

Abstract

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasi-stationary states (QSS), i.e. long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation". The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behaviour in phase space as the Vlasov system.

10 pages, 11 figures

References in corpus (10)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Collisionless relaxation in non-neutral plasmas
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
• Quasi-stationary states in the self-gravitating sheet model
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Relaxation times of unstable states in systems with long range interactions
• Statistical mechanics of collisionless relaxation in a noninteracting system

Cited by in corpus (3)

• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• The vmf90 program for the numerical resolution of the Vlasov equation for mean-field systems
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect