Dynamics and nonequilibrium states in the Hamiltonian mean-field model: A closer look

Abstract

We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model, but no traces of quasistationarity are found during the earlier stages of the evolution. We point out the nonergodic properties of this system in the short-time range, which makes a standard statistical description unsuitable. New aspects of the evolution during the nonergodic regime, and of the energy distribution function in the final approach to equilibrium, are disclosed.

Cited by in corpus (20)

• Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
• What should a statistical mechanics satisfy to reflect nature?
• Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
• Stability and ensemble inequivalence in a globally coupled system
• On the diffusive anomalies in a long-range Hamiltonian system
• The stochastic process of equilibrium fluctuations, of a system with long range interactions
• Metastable states, anomalous distributions and correlations in the HMF model
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• Relaxation of a 1-D gravitational system
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
• A note on non-thermodynamical applications of non-extensive statistics
• Quasi-stationary trajectories of the HMF model: a topological perspective
• Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium
• Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures
• Conditions for predicting quasistationary states by rearrangement formula
• Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions
• Stability of thermodynamic and dynamical order in a system of globally coupled rotors
• Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters