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Non-ergodicity induced by isotropic random perturbation.

Kenji Matsumoto1

  • 1Department of Mathematics, Hokkaido University, Sapporo, Japan.

Chaos (Woodbury, N.Y.)
|August 30, 2003
PubMed
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Random perturbations in a two-well Hamiltonian system cause non-ergodic behavior, trapping orbits in one well. This phenomenon arises from differing orbital separation rates at well exits, impacting dynamical systems research.

Area of Science:

  • Statistical Physics
  • Dynamical Systems Theory
  • Computational Physics

Background:

  • Hamiltonian systems are fundamental in classical mechanics and chaos theory.
  • Ergodicity assumes systems explore all accessible states uniformly over time.
  • Non-ergodic behavior deviates from uniform state exploration, indicating memory or localization.

Purpose of the Study:

  • To investigate the impact of isotropic random perturbations on a two-well Hamiltonian system.
  • To identify the underlying mechanisms causing non-ergodic behavior in this system.
  • To analyze the role of orbital separation rates in preferential well occupation.

Main Methods:

  • Development of a two-well Hamiltonian model.
  • Introduction of isotropic random perturbations to the system.

Related Experiment Videos

  • Numerical simulations to track orbital trajectories and analyze their behavior.

    • Main Results:

    • Observed non-ergodic behavior where orbits preferentially remain in one of the two wells.
    • Demonstrated that this localization is not due to energy barriers but perturbation effects.
    • Quantified differences in orbital separation rates near the well exits as the cause.

    Conclusions:

    • Isotropic random perturbations can induce significant non-ergodic dynamics in simple Hamiltonian systems.
    • The asymmetry in orbital separation rates near critical points dictates long-term orbital localization.
    • Findings have implications for understanding transport and dynamics in complex, perturbed systems.