Relaxation times of unstable states in systems with long range interactions

Abstract

We consider several models with long-range interactions evolving via Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian Mean Field (HMF) model and perturbed HMF models with either global anisotropy or an on-site potential are studied both analytically and numerically. We find that in the magnetic phase, the initial zero magnetization state remains stable above a critical energy and is unstable below it. In the dynamically stable state, these models exhibit relaxation time scales that increase algebraically with the number $N$ of particles, indicating the robustness of the quasistationary state seen in previous studies. In the unstable state, the corresponding time scale increases logarithmically in $N$.

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References in corpus (5)

• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Lynden-Bell and Tsallis distributions for the HMF model
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• Incomplete equilibrium in long-range interacting systems
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model

Cited by in corpus (6)

• Core-halo distribution in the Hamiltonian Mean-Field Model
• Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
• Nonequilibrium stationary states of 3D self-gravitating systems
• Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath
• Topology of Collisionless Relaxation
• Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions