Statistical theory of quasi stationary states beyond the single water-bag case study

Abstract

An analytical solution for the out-of-equilibrium quasi-stationary states of the paradigmatic Hamiltonian Mean Field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-levels water-bag. The comparison is shown to return an excellent agreement.

References in corpus (3)

• 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
• Enhancement of particle trapping in the wave-particle interaction

Cited by in corpus (7)

• 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
• Beam-Plasma Instability and Fast Particles: the Lynden-Bell Approach
• Violent relaxation in the Hamiltonian Mean Field model: I. Cold collapse and effective dissipation
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Topology of Collisionless Relaxation
• Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model