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Multidimensional activated rate processes with slowly relaxing mode

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  • Berezhkovskii, A.M.
  • Zitserman, V.Yu.

Abstract

The multidimensional Kramers problem is considered in the case of highly anisotropic friction. As a development of our previous results involving the study of several new regimes of activated rate process, we construct a theory which incorporates all these regimes and treats the process in every case in a uniform manner. To do this we take advantage of the friction anisotropy and reduce the initial multidimensional Fokker-Planck equation to a set of two effective one-dimensional equations. These equations describe diffusive motion along the slow coordinate in two effective potential wells and inter-well transitions due to the fast coordinate motion. To calculate the rate constant on the basis of the set we use an original method which is a generalization of the Kramers method. As a result we obtain a new formula for the rate constant which depending on the friction anisotropy level is smoothly changed from the well-known Kramers-Langer formula to new ones obtained in our previous papers.

Suggested Citation

  • Berezhkovskii, A.M. & Zitserman, V.Yu., 1992. "Multidimensional activated rate processes with slowly relaxing mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(3), pages 519-550.
    • Handle: RePEc:eee:phsmap:v:187:y:1992:i:3:p:519-550
    DOI: 10.1016/0378-4371(92)90009-F
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    References listed on IDEAS

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    1. Miller, Tom W. & Stone, Bernell K., 1985. "Daily Cash Forecasting and Seasonal Resolution: Alternative Models and Techniques for Using the Distribution Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 335-351, September.
    2. Berezhkovskii, A.M. & Zitserman, V.Yu., 1990. "Activated rate processes in a multidimensional case. A new solution of the Kramers problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 166(3), pages 585-621.
    3. Kummel, Reiner & Schussler, Uwe, 1991. "Heat equivalents of noxious substances: a pollution indicator for environmental accounting," Ecological Economics, Elsevier, vol. 3(2), pages 139-156, July.
    4. C. Knessl & B. J. Matkowsky & Z. Schuss & C. Tier, 1990. "An Integral Equation Approach to the M/G/2 Queue," Operations Research, INFORMS, vol. 38(3), pages 506-518, June.
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