Core-halo quasi-stationary states in the Hamiltonian mean-field model (Q2813016)

The author introduces the basic notions needed to describe quasi-stationary state in long-range systems: phase mixing, violent relaxation and the \textit{D. Lynden-Bell} statistics [``Statistical mechanics of violent relaxation in stellar systems'', MNRAS 136, No. 1, 101--121 (1967; \url{doi:10.1093/mnras/136.1.101})]. The author defines the Hamiltonian mean-field model and explain its Boltzmann-Gibbs collision equilibrium structure as well as discusses the foundation of the theory of of double Lynden-Bell equilibria by using the Hamiltonian mean-field model, which is the simplest model of a long-range system. The author studies quasi-stationary states with a core-halo structure in the Hamiltonian mean-field model at low energies per particle. Finally, the author examine the deviation degree of the quasi- stationary states from the Lynden-Bell equilibrium and the completeness of the collision relaxation of the quasi- stationary states by using the Lynden-Bell entropy and the double Lynden-Bell entropy, respectively. In the appendixes, the author provides supplementary calculations.