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

Abstract

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.

arXiv comment5 pages, 4 figures

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Cited by in corpus (6)

• Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
• On the diffusive anomalies in a long-range Hamiltonian system
• Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
• Stationary point approach to the phase transition of the classical XY chain with power-law interactions
• Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model
• Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions