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Unstable decay and state selection.

A McKane1, M Tarlie

  • 1Department of Theoretical Physics, University of Manchester, England.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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This study introduces a novel path-integral method to calculate probabilities of metastable state occupation. The technique accurately predicts state selection in systems with noise and nonlinearities.

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • Investigating the decay of unstable states into multiple metastable states is crucial in various scientific fields.
  • Understanding state selection in systems with noise and nonlinearities presents significant theoretical challenges.

Purpose of the Study:

  • To develop and apply a path-integral technique for calculating occupation probabilities of metastable states.
  • To analyze the interplay between nonlinearities and noise in determining state selection outcomes.

Main Methods:

  • Utilizing path-integral techniques in the weak-noise limit.
  • Calculating occupation probabilities by identifying optimal paths and their fluctuations.
  • Applying the method to a system described by coupled Langevin equations.

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Main Results:

  • A novel method for calculating metastable state occupation probabilities is presented.
  • The interplay of nonlinearities and noise is shown to be critical, invalidating naive approximations.
  • The derived probabilities are simple and show good agreement with numerical simulations.

Conclusions:

  • The developed optimal path method provides a robust framework for analyzing state selection in complex systems.
  • This approach offers broad applicability to diverse areas including fluid dynamics, superconductivity, lasers, chemical reactions, and population dynamics.