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Uniform expansion of the transition rate in Kramers' problem

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Abstract

Kramers' model of diffusion over potential barriers, e.g., chemical reactions, based on the noise activated escape of a particle from a potential well, is considered. Kramers derived escape rates valid for intermediate and large damping, and in a separate analysis, for small damping. In the small damping limit, Kramers' intermediate result reduces to the transition state rate which does not agree with the small damping result. A new escape rate is derived that is uniformly valid for all values of the damping coefficient. The new rate reduces to Kramers' results in the appropriate limits and, in particular, connects Kramers' intermediate and small damping results.

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Author notes

  1. Z. Schuss

    Present address: Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel

  2. C. Tier

    Present address: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60680, Illinois

Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois

    B. J. Matkowsky, Z. Schuss & C. Tier

Authors
  1. B. J. Matkowsky
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  2. Z. Schuss
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  3. C. Tier
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Additional information

This work was partially supported by the Air Force Office of Scientific Research under Grant No. AFOSR-83-0086, U.S. Department of Energy under Grant No. DE-AC02-78ERO-4650, and the National Science Foundation under Grant No. MCS-83-00562. One of us (BJM) gratefully acknowledges the support of a John Simon Guggenheim Memorial Foundation Fellowship.

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Matkowsky, B.J., Schuss, Z. & Tier, C. Uniform expansion of the transition rate in Kramers' problem. J Stat Phys 35, 443–456 (1984). https://doi.org/10.1007/BF01014395

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  • DOI: https://doi.org/10.1007/BF01014395

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