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Drift by dichotomous Markov noise.

I Bena1, C Van den Broeck, R Kawai

  • 1Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

This study provides exact solutions for probability density and drift velocity in systems with dichotomous Markov noise. These findings apply even when dynamics cross unstable points, as shown with the rocking ratchet model.

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Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Stochastic Processes

Background:

  • Systems driven by noise exhibit complex behaviors.
  • Dichotomous Markov noise is a common model for random fluctuations.
  • Understanding asymptotic dynamics is crucial for predicting long-term system behavior.

Purpose of the Study:

  • Derive explicit analytical results for asymptotic probability density and drift velocity.
  • Investigate systems with dichotomous Markov noise, including transitions through unstable fixed points.
  • Illustrate the derived results using the rocking ratchet problem.

Main Methods:

  • Analytical derivation of probability density functions.
  • Calculation of drift velocity using stochastic calculus.

Related Experiment Videos

  • Analysis of systems crossing unstable fixed points.

    • Main Results:

    • Explicit formulas for asymptotic probability density and drift velocity were obtained.
    • The method successfully handles cases where asymptotic dynamics cross unstable fixed points.
    • The rocking ratchet model serves as a clear illustration of the theoretical results.

    Conclusions:

    • The derived results offer a precise mathematical framework for analyzing stochastic systems.
    • The approach is applicable to a range of physical systems exhibiting dichotomous Markov noise.
    • This work advances the understanding of noise-induced phenomena in nonlinear systems.