Modified Kramers formulas for the decay rate in agreement with dynamical modeling

E. G. Pavlova, N. E. Aktaev, I. I. Gontchar

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.

    Original languageEnglish
    Pages (from-to)6084-6100
    Number of pages17
    JournalPhysica A: Statistical Mechanics and its Applications
    Volume391
    Issue number23
    DOIs
    Publication statusPublished - 1 Dec 2012

    Fingerprint

    Decay Rate
    decay rates
    Metastable States
    Modeling
    Small Parameter
    Brownian motion
    Friction
    Stiffness
    Extremes
    Derivative
    Energy
    borders
    thermal energy
    metastable state
    stiffness
    friction

    Keywords

    • Corrections to Kramers formulas
    • Decay rate
    • Kramers rate
    • Metastable system

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Statistics and Probability

    Cite this

    Modified Kramers formulas for the decay rate in agreement with dynamical modeling. / Pavlova, E. G.; Aktaev, N. E.; Gontchar, I. I.

    In: Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 23, 01.12.2012, p. 6084-6100.

    Research output: Contribution to journalArticle

    Pavlova, E. G. ; Aktaev, N. E. ; Gontchar, I. I. / Modified Kramers formulas for the decay rate in agreement with dynamical modeling. In: Physica A: Statistical Mechanics and its Applications. 2012 ; Vol. 391, No. 23. pp. 6084-6100.
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