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Anomalous jumping in a double-well potential.

P D Ditlevsen1

  • 1The Niels Bohr Institute, Department for Geophysics, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen O, Denmark.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Extreme noise events, like Levy flights, can trigger transitions between states. This phenomenon, driven by alpha-stable noise, influences geophysical and climatic changes and results in non-Gibbs distributions.

Area of Science:

  • Physics
  • Complex Systems
  • Geophysics

Background:

  • Metastable states are common in physical and natural systems.
  • Noise can induce transitions between these states, but the effect of noise structure is not fully understood.

Purpose of the Study:

  • To investigate the role of alpha-stable noise in inducing transitions between metastable states.
  • To analyze the impact of noise structure on transition probabilities and steady-state statistics.

Main Methods:

  • Theoretical analysis of systems subjected to alpha-stable noise.
  • Investigation of Levy flights as a mechanism for state transitions.
  • Examination of steady-state distributions under alpha-stable noise conditions.

Main Results:

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  • Single extreme events in alpha-stable noise, known as Levy flights, significantly contribute to transition probabilities.
  • The structure of alpha-stable noise leads to non-Gibbs steady-state distributions.
  • These findings have potential implications for understanding sudden changes in geophysical flows and climate.

Conclusions:

  • Alpha-stable noise fundamentally alters the dynamics of metastable systems.
  • Levy flights are a key mechanism for noise-induced transitions with potential geophysical and climatic relevance.
  • The resulting non-Gibbsian statistics highlight the importance of considering noise structure in complex systems.