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Collective oscillation in a hamiltonian system.

Hidetoshi Morita1, Kunihiko Kaneko

  • 1Faculty of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan. morita@aoni.waseda.jp

Physical Review Letters
|February 21, 2006
PubMed
Summary

Macroscopic variable oscillations emerge in metastable Hamiltonian systems. This collective motion, driven by self-organization, lasts longer as system size increases, revealing universal phenomena.

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Area of Science:

  • Statistical mechanics
  • Dynamical systems theory
  • Nonlinear physics

Background:

  • Metastable states in Hamiltonian systems are typically associated with equilibrium or slow relaxation.
  • Collective phenomena in physical systems often arise from complex interactions and self-organization.
  • Hopf bifurcation is a known mechanism for generating oscillations in dissipative systems.

Purpose of the Study:

  • To investigate the emergence and characteristics of oscillations in the metastable state of a mean-field Hamiltonian system.
  • To understand the underlying mechanism driving this collective motion.
  • To explore the universality of the observed phenomena across different system sizes.

Main Methods:

  • Analysis of macroscopic variable oscillations in a metastable Hamiltonian system.
  • Investigation of the system's behavior through Hopf bifurcation.
  • Self-consistent analysis of the distribution function to explain the oscillation's origin.
  • Systematic study of the oscillation's duration dependence on system size.

Main Results:

  • Discovery of oscillation in macroscopic variables within the metastable state.
  • Observed divergence in oscillation duration with increasing system size.
  • Identification of Hopf bifurcation as the route to this collective motion.
  • Explanation of oscillation as self-organization of a self-excited swing state via the mean field.

Conclusions:

  • Metastable states in Hamiltonian systems can exhibit long-lasting collective oscillations.
  • The observed phenomena demonstrate a self-organization mechanism leading to emergent dynamics.
  • The universality of these oscillations suggests broader implications in various physical systems.

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