Skip to main content
SpringerLink
Log in

First Passage Time Renormalization and Escape from an Imperfect Trap

  • Chapter
New Trends in Kramers’ Reaction Rate Theory

Part of the book series: Understanding Chemical Reactivity ((UCRE,volume 11))

  • 244 Accesses

Abstract

We review renormalization techniques applied to random walks on self-similar structures. It is shown that the escape of a particle out of a large region surrounding an imperfect trap obeys an exponential law provided the random walk is recurrent and the diffusion time can be neglected.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Wilson, Rev. Mod. Phys. 47, 773 (1975).

    Article  Google Scholar 

  2. M. J. Feigenbaum, J. Stat. Phys. 21, 669 (1979).

    Article  Google Scholar 

  3. J. Machta, Phys. Rev. B 24, 5260 (1981)

    Article  Google Scholar 

  4. J. Machta, J. Phys. A 18, L531 (1985)

    Article  Google Scholar 

  5. S. Robillard and A.-M. Tremblay, J. Phys. A 19, 2171 (1986)

    Article  Google Scholar 

  6. S. Alexander and R. Orbach, J. Physique Lett. 43, L625 (1982)

    Article  Google Scholar 

  7. R. Khang and S. Redner, J. Phys. A 22, 887 (1989)

    Article  Google Scholar 

  8. C. Van den Broeck and T. Tel, in From Phase Transitions to Chaos: Modern Topics in Statistical Physics, G. Gyorgyi, I. Kondor, L. Sasvari, and T. Tel (Eds.), World Scientific, Singapore (1992), pp. 227–236.

    Google Scholar 

  9. C. Van den Broeck, Phys. Rev. Lett. 62, 1421 (1989)

    Article  Google Scholar 

  10. C. Van den Broeck, Phys. Rev. A 40, 7334 (1989).

    Article  Google Scholar 

  11. C. Van den Broeck, in Irreversible Processes and Selforganization, W. Ebeling and H. Ullbricht (Eds.), Teubner-Verlag, Leipzig (1989), pp. 57–64.

    Google Scholar 

  12. J. M. R. Parrondo, H. L. Martínez, R. Kawai, and K. Lindenberg, Phys. Rev. A 42, 723 (1990).

    Article  Google Scholar 

  13. C. Van den Broeck and V Balakrishnan, Zeitschr. f. Phys. Chem. 95, 342 (1991).

    Google Scholar 

  14. C. Van den Broeck, J. Stat. Phys. 65, 971 (1991).

    Article  Google Scholar 

  15. S. Havlin and D. Ben-Avraham, Adv. Phys. 36, 695 (1987).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep. Física Aplicada I, Universidad Complutense, 28040, Madrid, Spain

    J. M. R. Parrondo

Authors
  1. C. Van Den Broeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. R. Parrondo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Paul Scherrer Institute, Villingen, Switzerland

    Peter Talkner

  2. Department of Physics, Universität Augsburg, Augsburg, Germany

    Peter Hänggi

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Van Den Broeck, C., Parrondo, J.M.R. (1995). First Passage Time Renormalization and Escape from an Imperfect Trap. In: Talkner, P., Hänggi, P. (eds) New Trends in Kramers’ Reaction Rate Theory. Understanding Chemical Reactivity, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0465-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0465-4_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4208-6

  • Online ISBN: 978-94-011-0465-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation