Spectral Definition of the Characteristic Times for Anomalous Diffusion in a Potential

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


Characteristic times of the noninertial fractional diffusion of a particle in a potential are defined in terms of three time constants, viz., the integral, effective, and longest relaxation times. These times are described using the eigenvalues of the corresponding Fokker-Planck operator for the normal diffusion. Knowledge of them is sufficient to accurately predict the anomalous relaxation behavior for all time scales of interest. As a particular example, we consider the subdiffusion of a planar rotor in a double-well potential.


Relaxation Function Anomalous Diffusion Normal Diffusion Continuous Time Random Walk Longe Relaxation Time 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Yuri P. Kalmykov
    • 1
  • William T. Coffey
    • 2
  • Serguey V. Titov
    • 3
  1. 1.Laboratoire de Mathématiques et PhysiqueUniversité de Perpignan Via DomitiaPerpignanFrance
  2. 2.Department of Electronic and Electrical EngineeringTrinity CollegeDublin 2Ireland
  3. 3.Kotelnikov Institute of Radio Engineering and ElectronicsRussian Academy of SciencesFryazinoRussian Federation

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