Bistability driven by weakly colored Gaussian noise: The Fokker-Planck boundary layer and mean first-passage times
Journal Article
·
· Phys. Rev. Lett.; (United States)
We develop a singular perturbation approach to the problem of first-passage times for non-Markovian processes driven by Gaussian colored noise near the white-noise limit. In particular we treat the problem of overdamped tunneling in a bistable quartic potential in the presence of Gaussian noise of short correlation time tau. The correct treatment of the absorbing boundary yields a lowest-order correction proportional to tau/sup 1/2/ with a proportionality constant involving the Milne extrapolation length for the Fokker-Planck equation, given in terms of the Riemann zeta function.
- Research Organization:
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
- DOE Contract Number:
- W-7405-ENG-36; W-7405-ENG-48
- OSTI ID:
- 5852797
- Journal Information:
- Phys. Rev. Lett.; (United States), Vol. 59:19
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
STOCHASTIC PROCESSES
PERTURBATION THEORY
BOUNDARY LAYERS
CORRELATIONS
FOKKER-PLANCK EQUATION
GAUSSIAN PROCESSES
HERMITE POLYNOMIALS
NOISE
NONLINEAR PROBLEMS
TUNNEL EFFECT
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
LAYERS
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
657000* - Theoretical & Mathematical Physics
GENERAL PHYSICS
STOCHASTIC PROCESSES
PERTURBATION THEORY
BOUNDARY LAYERS
CORRELATIONS
FOKKER-PLANCK EQUATION
GAUSSIAN PROCESSES
HERMITE POLYNOMIALS
NOISE
NONLINEAR PROBLEMS
TUNNEL EFFECT
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
LAYERS
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
657000* - Theoretical & Mathematical Physics