Topology of Collisionless Relaxation

Abstract

Using extensive molecular dynamics simulations we explore the fine-grained phase space structure of systems with long-range interactions. We find that if the initial phase space particle distribution has no holes, the final stationary distribution will also contain a compact simply connected region. The microscopic holes created by the filamentation of the initial distribution function are always restricted to the outer regions of the phase space. In general, for complex multilevel distributions it is very difficult to a priori predict the final stationary state without solving the full dynamical evolution. However, we show that for multilevel initial distributions satisfying a generalized virial condition, it is possible to predict the particle distribution in the final stationary state using Casimir invariants of the Vlasov dynamics.

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• 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
• Relaxation times of unstable states in systems with long range interactions