High-Frequency Resonance Absorption as Evidence for Oscillation in a Well Before Escape from a Metastable State in the Kramers Energy Controlled Diffusion Model

  • William T. Coffey
  • Yuri P. Kalmykov
  • Serguey V. Titov
  • D. S. F. Crothers
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)

Abstract

A variety of disparate physical systems which are modeled in terms of their relaxation behavior by the Brownian motion in a potential and its extensions to anomalous diffusion exhibit slow overbarrier relaxation accompanied by relatively fast relaxation due to exponential decays in the potential wells and high frequency resonance absorption due to small oscillations about the minima of the wells. It is argued that the high frequency resonant process provides abundant evidence for the Kramers concept of oscillations in a potential well of particles with energy equal to the separatrix energy before escape as both are simply limiting cases of the same family of librational dynamical processes in a well.

Keywords

Langevin Equation Anomalous Diffusion Transition State Theory Escape Rate Transition State Theory 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • William T. Coffey
    • 1
  • Yuri P. Kalmykov
    • 2
  • Serguey V. Titov
    • 3
  • D. S. F. Crothers
    • 4
  1. 1.Department of Electronic and Electrical EngineeringTrinity CollegeDublin 2Ireland
  2. 2.Laboratoire de Mathématiques et PhysiqueUniversité de Perpignan Via DomitiaPerpignan CedexFrance
  3. 3.Kotelnikov Institute of Radio Engineering and ElectronicsRussian Academy of SciencesFryazinoRussian Federation
  4. 4.Department of Applied Mathematics and Theoretical PhysicsQueen’s University BelfastBelfastNorthern Ireland

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