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Related Experiment Videos

Escape driven by alpha-stable white noises.

B Dybiec1, E Gudowska-Nowak, P Hänggi

  • 1M. Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. bartek@th.if.uj.edu.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary
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Brownian particles in double wells escape faster with Lévy noise, unlike normal diffusion. Noise-induced jumps alter escape dynamics and mean first passage time calculations.

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Stochastic Processes

Background:

  • Investigates escape dynamics in a symmetric double well potential.
  • Focuses on systems driven by white Lévy noise, neglecting inertial effects.
  • Highlights the unique behavior of generalized Brownian paths with noise-induced jumps.

Purpose of the Study:

  • To analyze escape trajectories and mean first passage time (MFPT) under Lévy noise.
  • To understand how Lévy noise parameters (alpha, beta) influence escape rates.
  • To compare MFPT boundary conditions with those in normal diffusion.

Main Methods:

  • Numerical implementation of boundary conditions for MFPT.
  • Analysis of survival probability and average escape time.

Related Experiment Videos

  • Investigation of noise-induced discontinuities in generalized Brownian paths.

    • Main Results:

    • Lévy noise can enhance or suppress escape rates depending on skewness (beta).
    • Escape rate shows non-monotonic behavior and discontinuity at alpha=1.
    • The typical MFPT ratio (2:1) for normal diffusion does not hold.
    • Survival probabilities exhibit exponential behavior for high barriers and deviations for low barriers.

    Conclusions:

    • Lévy noise fundamentally alters escape dynamics compared to normal diffusion.
    • The discontinuity in generalized Brownian paths necessitates modified MFPT boundary conditions.
    • Lévy noise parameters offer tunable control over escape phenomena in stochastic systems.