Inertial effects on the escape rate of a particle driven by colored noise

an instanton approach

T. J. Newman, A. J. Bray, A. J. McKane

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation {Mathematical expression}, where ? is a Gaussian colored noise with mean zero and correlator =(D/t)exp(-|t-t'|/t). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D?0) limit. This yields an escape rate G~exp(-S/D), where the "action"S is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an "instanton" of the theory. The extremal action S is calculated analytically for small m and t for general potentials, and numerical results for S are displayed for various ranges of m and t for the typical case of the quartic potential V(x)=-x/2+x/4.
    Original languageEnglish
    Pages (from-to)357-369
    Number of pages13
    JournalJournal of Statistical Physics
    Volume59
    Issue number1-2
    DOIs
    Publication statusPublished - Apr 1990

    Fingerprint

    Escape Rate
    Colored Noise
    Langevin Equation
    Instantons
    instantons
    escape
    Path
    Steepest Descent
    Correlator
    Quartic
    descent
    Valid
    random noise
    correlators
    Numerical Results
    Formulation
    Zero
    Term
    Range of data
    formulations

    Cite this

    Newman, T. J. ; Bray, A. J. ; McKane, A. J. / Inertial effects on the escape rate of a particle driven by colored noise : an instanton approach. In: Journal of Statistical Physics. 1990 ; Vol. 59, No. 1-2. pp. 357-369.
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    abstract = "A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation {Mathematical expression}, where ? is a Gaussian colored noise with mean zero and correlator =(D/t)exp(-|t-t'|/t). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D?0) limit. This yields an escape rate G~exp(-S/D), where the {"}action{"}S is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an {"}instanton{"} of the theory. The extremal action S is calculated analytically for small m and t for general potentials, and numerical results for S are displayed for various ranges of m and t for the typical case of the quartic potential V(x)=-x/2+x/4.",
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    Inertial effects on the escape rate of a particle driven by colored noise : an instanton approach. / Newman, T. J.; Bray, A. J.; McKane, A. J.

    In: Journal of Statistical Physics, Vol. 59, No. 1-2, 04.1990, p. 357-369.

    Research output: Contribution to journalArticle

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