Journal of Statistical Physics

, Volume 63, Issue 1–2, pp 47–58 | Cite as

Fluctuations in the motions of mass and of patterns in one-dimensional driven diffusive systems

  • H. van Beijeren


The stochastic spreading of mass fluctuations in systems described by a fluctuating Burgers equation increases ast2/3 with time. As a consequence the stochastic motion of a mass front, a point through which no excess mass current is flowing, is shown to increase ast1/3. The same is true for the stochastic displacement of mass points and shock fronts with respect to their average drift, provided the initial configuration is fixed. An additional average over the stationary distribution of the initial configuration yields stochastic displacements, increasing with time ast1/2.

Key words

Burgers equation (fluctuating) diffusion (anomalous) density fluctuations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. de Masi and P. A. Ferrari,J. Stat. Phys. 38:603 (1985).Google Scholar
  2. 2.
    H. van Beijeren and R. Kutner,J. Stat. Phys. 39:317 (1985).Google Scholar
  3. 3.
    J. Gartner and E. Presutti, Shock fluctuations in a particle system, preprint.Google Scholar
  4. 4.
    D. Forster, D. R. Nelson, and M. J. Stephen,Phys. Rev. A 16:732 (1977).Google Scholar
  5. 5.
    H. van Beijeren, H. Spohn, and R. Kutner,Phys. Rev. Lett. 54:2026 (1985).Google Scholar
  6. 6.
    P. A. Ferrari, C. Kipnis, and E. Saada, Microscopic structure of travelling waves in the asymmetric simple exclusion process.Google Scholar
  7. 7.
    P. A. Ferrari, Private communication.Google Scholar
  8. 8.
    T. E. Harris,J. Appl. Prob. 2:323 (1965).Google Scholar
  9. 9.
    S. Alexander and P. Pincus,Phys. Rev. B 18:2011 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • H. van Beijeren
    • 1
  1. 1.Institute for Theoretical PhysicsTA UtrechtThe Netherlands

Personalised recommendations