Bistability driven by weakly colored Gaussian noise: The Fokker-Planck boundary layer and mean first-passage times

Journal Article · Mon Nov 09 04:00:00 EST 1987 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.59.2129· OSTI ID:5852797

Doering, C R; Hagan, P S; Levermore, C D

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), Journal Name: Phys. Rev. Lett.; (United States) Vol. 59:19; ISSN PRLTA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY LAYERS
CORRELATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FOKKER-PLANCK EQUATION
FUNCTIONS
GAUSSIAN PROCESSES
HERMITE POLYNOMIALS
LAYERS
NOISE
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POLYNOMIALS
STOCHASTIC PROCESSES
TUNNEL EFFECT