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Related Experiment Videos

Symmetry breaking in one-dimensional diffusion

Gitterman1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
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Stochastic resonance occurs in one-dimensional diffusion when a deterministic telegraph signal breaks symmetry. Increasing signal asymmetry broadens the parameter range for this phenomenon.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • One-dimensional diffusion is a fundamental process in statistical mechanics.
  • Deterministic telegraph signals introduce periodic switching between two states.
  • Stochastic resonance describes a phenomenon where noise enhances signal transmission.

Purpose of the Study:

  • To investigate the mean free passage time for one-dimensional diffusion under a deterministic telegraph signal.
  • To explore the conditions and impact of symmetry breaking on this diffusion process.
  • To analyze the relationship between signal asymmetry and the occurrence of stochastic resonance.

Main Methods:

  • Mathematical modeling of one-dimensional diffusion on a line segment.
  • Incorporation of a deterministic telegraph signal with controllable asymmetry.

Related Experiment Videos

  • Analysis of the mean free passage time as a function of signal rate and asymmetry.
  • Examination of symmetry breaking through nonsymmetric boundary conditions or signal properties.

    • Main Results:

    • The mean free passage time exhibits nonmonotonic behavior with respect to the signal rate, indicating stochastic resonance.
    • Symmetry breaking, either in boundary conditions or the telegraph signal, is crucial for observing this resonance.
    • A larger asymmetry in the telegraph signal leads to a wider parameter range where stochastic resonance is observed.

    Conclusions:

    • Symmetry breaking is a key factor enabling stochastic resonance in one-dimensional diffusion driven by a deterministic telegraph signal.
    • The degree of telegraph signal asymmetry directly influences the conditions under which stochastic resonance occurs.
    • This study provides insights into the interplay between signal characteristics, boundary conditions, and emergent phenomena in diffusion processes.