On the Formation of a Quasi-stationary Non-Traveling cluster in the Attractive Hamiltonian Mean-Field Model

Long-range interacting systems usually exhibit quasi-stationary states that deviate from thermal equilibrium over extended periods of time. In particular, in the attractive Hamiltonian mean-field (HMF) model, one of these states is characterized by traveling clusters of particles in the phase-space, generated by the resonance with two counter-propagating density waves. Here, we report the existence of a third, non-traveling cluster, and we explain its formation by the existence of a stationary wave in the system which is generated as a product of a linear superposition of the other two counter-propagating waves.