Journal of Statistical Physics

, Volume 43, Issue 3–4, pp 561–570 | Cite as

Escape times in interacting biased random walks

  • Mustansir Barma
  • Ramakrishna Ramaswamy
Articles

Abstract

The dynamics ofN particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on theN sites of the lattice closest to the wall. ForN=1 the leading behavior of the first passage timeTFP to a distant sitel is known to follow the Kramers escape time formulaTFPλl whereλ is the ratio of hopping rates toward and away from the wall. ForN > 1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes toTFRλIN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival timesTs in the presence of an absorbing barrier placed at sitel. In contrast to the first passage time, it is found thatTs follows the leading behaviorλ′ independent ofN.

Key words

Interacting random walks bias generalized Kramers escape problem survival times 

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References

  1. 1.
    H. A. Kramers,Physica 7:284 (1940).Google Scholar
  2. 2.
    S. Chandrasekhar,Rev. Mod. Phys. 15:1 (1943).Google Scholar
  3. 3.
    S. Dattagupta and S. R. Shenoy, Stochastic Processes: Formalism and Applications, Lecture Notes in Physics (Springer-Verlag, New York, 1983), Vol. 184, p. 61.Google Scholar
  4. 4.
    Z. Schuss,SIAM J. Rev. 22:119 (1980).Google Scholar
  5. 5.
    H. Bottger and V. V. Bryskin,Physica Stat. Solidi B113:9 (1982).Google Scholar
  6. 6.
    M. Barma and D. Dhar,J. Phys. C16:1451 (1983).Google Scholar
  7. 7.
    T. Ohtsuki and T. Keyes,Phys. Rev. Lett. 52:1177 (1984).Google Scholar
  8. 8.
    S. R. White and M. Barma,J. Phys. A17:2995 (1984).Google Scholar
  9. 9.
    M. Barma,Proc. Solid State Phys. Symp. (India) 27C:111 (1984).Google Scholar
  10. 10.
    D. Griffeath, Additive and Cancellative Interaction Particle Systems, Lecture Notes in Mathematics, No. 724 (Springer-Verlag, New York, 1979); T. M. Liggett,Interacting Particle Systems (Springer-Verlag, New York, 1985).Google Scholar
  11. 11.
    M. E. Fisher,J. Stat. Phys. 34:667 (1984).Google Scholar
  12. 12.
    S. Katz, J. L. Lebowitz, and H. Spohn,J. Stat. Phys. 34:497 (1984).Google Scholar
  13. 13.
    M. Khantha and V. Balakrishnan,Pramana 21:111 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Mustansir Barma
    • 1
  • Ramakrishna Ramaswamy
    • 1
  1. 1.Tata Institute of Fundamental ResearchBombayIndia

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