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.

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Cited by in corpus (5)

• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model