On the effectiveness of mixing in violent relaxation

TL;DR

This paper investigates the relaxation mechanisms in collisionless systems with long-range interactions, demonstrating stretching and folding behaviors that lead to quasi-stationary states, using numerical simulations and simplified maps.

Contribution

It reveals a plausible relaxation mechanism involving stretching and folding, connecting Vlasov dynamics with area-preserving maps.

Findings

Stretching and folding observed in Vlasov simulations

Similar behavior found in mean-field maps

Provides insight into violent relaxation process

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.