Quasi-stationary trajectories of the HMF model: a topological perspective

We employ a topological approach to investigate the nature of quasi-stationary states of the Mean Field XY Hamiltonian model that arise when the system is initially prepared in a fully magnetized configuration. By means of numerical simulations and analytical considerations, we show that, along the quasi-stationary trajectories, the system evolves in a manifold of critical points of the potential energy function. Although these critical points are maxima, the large number of directions with marginal stability may be responsible for the slow relaxation dynamics and the trapping of the system in such trajectories.