Random fluctuation leads to forbidden escape of particles

Research output: Contribution to journalArticle

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Abstract

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Kolmogorov-Arnold-Moser (KAM) islands escape within finite time. The nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperboliclike time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate these phenomena with a numerical study applying random maps.
Original languageEnglish
Article number026211
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume82
Issue number2
DOIs
Publication statusPublished - 27 Aug 2010

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escape
trajectories
Trajectory
Fluctuations
Scattering
Random Maps
hyperbolic systems
Physical process
decay
Hyperbolic Systems
Exponential Decay
guy wires
scattering
random walk
Fractal Dimension
Numerical Study
fractals
Random walk
Power Law
Decay

Keywords

  • Saturns rings
  • complexity

Cite this

Random fluctuation leads to forbidden escape of particles. / Rodrigues, Christian; de Moura, Alessandro Paula Servio; Grebogi, Celso.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 82, No. 2, 026211, 27.08.2010.

Research output: Contribution to journalArticle

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