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Clusters die hard: Time-correlated excitation in the Hamiltonian mean field model

Koyama H.
•
Konishi T.
•
Ruffo, Stefano
2008
  • journal article

Periodico
COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION
Abstract
The Hamiltonian mean field (HMF) model has a low-energy phase where N particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the "fully-clustered" and "excited" dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the Vlasov equation associated with the N → ∞ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the "fully-clustered" and "excited" states appear in turn. We find that the distribution of the lifetime of the "fully-clustered" state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where itinerancy among different "quasi-stationary" states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions. © 2006 Elsevier B.V. All rights reserved.
DOI
10.1016/j.cnsns.2006.08.006
WOS
WOS:000254602200003
Archivio
http://hdl.handle.net/20.500.11767/12249
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-36248974190
http://www.sciencedirect.com/science/article/pii/S1007570406001730
Diritti
metadata only access
Soggetti
  • Chaotic dynamics

  • Statistical mechanics...

  • Cluster dynamics

  • Chaotic itinerancy

  • Settore FIS/03 - Fisi...

Scopus© citazioni
2
Data di acquisizione
Jun 7, 2022
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Web of Science© citazioni
3
Data di acquisizione
Mar 24, 2024
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Data di acquisizione
Apr 19, 2024
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