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Channeling and percolation in two-dimensional chaotic dynamics.

D. K. Chaikovsky1, G. M. Zaslavsky

  • 1Institute of Space Research, Academy of Sciences of the USSR, Profsoyuznaya 84/32, Moscow 117810, USSR.

Chaos (Woodbury, N.Y.)
|December 1, 1991
PubMed
Summary

This study analyzes particle motion in a 2-D potential, revealing two types of random walks: stochastic channeling and percolation. Anomalous transport and intermittency characterize particle movement across different energy levels.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Hamiltonian dynamics describes particle motion governed by energy.
  • Nearly periodic potentials with square symmetry create complex particle behaviors.
  • Stochastic processes, like random walks, are crucial in understanding particle transport.

Purpose of the Study:

  • To analyze the Hamiltonian dynamics of a particle in a nearly periodic 2-D potential.
  • To investigate the emergence and characteristics of two distinct types of unbounded random walks.
  • To determine the conditions and energy thresholds for stochastic percolation and anomalous transport.

Main Methods:

  • Analysis of Hamiltonian dynamics for a particle in a 2-D potential.
  • Identification and characterization of quasi-1-D (stochastic channeling) and 2-D (stochastic percolation) random walks.

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  • Investigation of intermittency and anomalous transport phenomena.

    • Main Results:

    • Two types of unbounded random walks were identified: stochastic channeling and stochastic percolation.
    • A scenario for the onset of stochastic percolation was analyzed, with a threshold energy dependent on the perturbation parameter.
    • Both random walk types exhibit intermittency, leading to anomalous particle transport in specific energy intervals.

    Conclusions:

    • The study elucidates complex particle dynamics in a specific 2-D potential.
    • Stochastic channeling and percolation represent key mechanisms for particle transport.
    • Intermittency and anomalous transport are significant features of particle motion in this system.