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Journal of Statistical Physics

, Volume 50, Issue 5–6, pp 1271–1276 | Cite as

On the field dependence of random walks in the presence of random fields

  • A. Bunde
  • S. Havlin
  • H. E. Roman
  • G. Schildt
  • H. E. Stanley
Short Communications

Abstract

Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or −E. The probability density¯P(x, t) is found to scale asymptotically as
$$\left\{ {[A(E)]^{\beta /2} /\ln ^2 t} \right\}\exp \left( { - \left\{ {x[A(E)]^{\beta /2} /\ln ^2 t} \right\}^\alpha } \right)$$
withA(E)=ln[(1+E)/(1-E)],β=4.25, and α=1.25. The mean square displacement scales as\(\langle x^2 \rangle \sim [A(E)]^{ - \beta } F[tA^\beta (E)]\), where F(u)∼ln4u asymptotically.

Key words

Random walks random fields density distribution fluctuations anomalous diffusion 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • A. Bunde
    • 1
    • 2
  • S. Havlin
    • 1
    • 2
  • H. E. Roman
    • 3
    • 4
  • G. Schildt
    • 1
  • H. E. Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBoston
  2. 2.Department of PhysicsBar-Ilan UniversityRamat-GanIsrael
  3. 3.Fakultät für PhysikUniversität KonstanzKonstanzFederal Republic of Germany
  4. 4.Institut für Theoretische PhysikUniversität HamburgHamburg 36Federal Republic of Germany

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