Double Lynden-Bell structure of low-energy quasistationary distributions in the Hamiltonian mean-field model.

In the Hamiltonian mean-field model, we study the core-halo structure of low-energy quasistationary states under unsteady water-bag type initial conditions. The core-halo structure results in the superposition of two independent Lynden-Bell distributions. We examine the completeness of the Lynden-Bell relaxation and the relaxation between these two Lynden-Bell distributions.