Critical behavior of the Kramers escape rate in asymmetric classical field theories

D. L. Stein

    Research output: Contribution to journalArticle

    Abstract

    We introduce an asymmetric classical Ginzburg-Landau model in a bounded interval, and study its dynamical behavior when perturbed by weak spatiotemporal noise. The Kramers escape rate from a locally stable state is computed as a function of the interval length. An asymptotically sharp second-order phase transition in activation behavior, with corresponding critical behavior of the rate prefactor, occurs at a critical length ℓc, similar to what is observed in symmetric models. The weak-noise exit time asymptotics, to both leading and subdominant orders, are analyzed at all interval lengthscales. The divergence of the prefactor as the critical length is approached is discussed in terms of a crossover from non-Arrhenius to Arrhenius behavior as noise intensity decreases. More general models without symmetry are observed to display similar behavior, suggesting that the presence of a "phase transition" in escape behavior is a robust and widespread phenomenon.

    Original languageEnglish (US)
    Pages (from-to)1537-1556
    Number of pages20
    JournalJournal of Statistical Physics
    Volume114
    Issue number5-6
    StatePublished - Mar 2004

    Fingerprint

    Classical Field Theory
    Escape Rate
    Critical Behavior
    escape
    Interval
    Phase Transition
    intervals
    Exit Time
    Ginzburg-Landau Model
    Dynamical Behavior
    Length Scale
    Crossover
    Activation
    Divergence
    noise intensity
    Symmetry
    Decrease
    crossovers
    divergence
    activation

    Keywords

    • Droplet nucleation
    • False vacuum
    • Fluctuation determinant
    • Fokker-Planck equation
    • Instanton
    • Non-Arrhenius behavior
    • Spatiotemporal noise
    • Stochastic escape problem
    • Stochastic exit problem
    • Stochastically perturbed dynamical systems

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics

    Cite this

    Critical behavior of the Kramers escape rate in asymmetric classical field theories. / Stein, D. L.

    In: Journal of Statistical Physics, Vol. 114, No. 5-6, 03.2004, p. 1537-1556.

    Research output: Contribution to journalArticle

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