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Streaminglike diffusion in the low-dimensional stochastic pump model.

G Corso1, A J Lichtenberg

  • 1Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, CA 94720, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Diffusion in Hamiltonian systems can follow power laws related to coupling, not stochasticity. This resonance streaming diffusion is distinct from Arnold diffusion and explains recent findings in coupled standard maps.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • Hamiltonian systems exhibit complex dynamics, including diffusion.
  • Arnold diffusion describes slow particle drift across resonances in conservative systems.
  • Coupled mappings are used to model various physical phenomena.

Purpose of the Study:

  • To analyze diffusion in a few-dimensional Hamiltonian system of coupled mappings.
  • To investigate the role of resonances in diffusion processes.
  • To compare resonance streaming diffusion with Arnold diffusion.

Main Methods:

  • Analysis of a few-dimensional Hamiltonian system of coupled mappings.
  • Investigating diffusion along resonances.
  • Comparing diffusion dependence on coupling (μ) and stochastic (K) parameters.

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Main Results:

  • Diffusion primarily occurs along resonances.
  • Diffusion exhibits a power-law dependence on the coupling parameter μ.
  • Diffusion is independent of the stochastic parameter K.
  • Resonance streaming diffusion can be significantly larger than Arnold diffusion for certain parameters.

Conclusions:

  • Resonance streaming diffusion provides a mechanism for rapid transport in Hamiltonian systems.
  • The findings qualitatively explain recent results in multidimensional coupled standard maps.
  • Diffusion behavior is strongly influenced by resonant structures.