Path integrals and non-Markov processes. II. Escape rates and stationary distributions in the weak-noise limit

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

    Research output: Contribution to journalArticle

    59 Citations (Scopus)

    Abstract

    The path-integral formalism developed in the preceding paper [McKane, Luckock, and Bray, Phys. Rev. A 41, 644 (1990)] is used to calculate, in the weak-noise limit, the rate of escape of a particle over a one-dimensional potential barrier, for exponentially correlated noise (t)(t) =(D/)exp{-t-t/}. For small D, a steepest-descent evaluation of the appropriate path integral yields exp(-S/D), where S is the action associated with the dominant (instanton) path. Analytical results for S are obtained for small and large , and (essentially exact) numerical results for intermediate. The stationary joint probability density for the position and velocity of the particle is also calculated for small D: it has the form Pst (x,xI)exp[-S(x,xI)/D]. Results are presented for the marginal probability density Pst(x) for the position of the particle.
    Original languageEnglish
    Pages (from-to)657-667
    Number of pages11
    JournalPhysical Review A
    Volume41
    Issue number2
    DOIs
    Publication statusPublished - Jan 1990

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