Journal of Statistical Physics

, Volume 73, Issue 5–6, pp 813–842 | Cite as

Exact solution of the totally asymmetric simple exclusion process: Shock profiles

  • B. Derrida
  • S. A. Janowsky
  • J. L. Lebowitz
  • E. R. Speer


The microscopic structure of macroscopic shocks in the one-dimensional, totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles-“first” and “second” class. This nonequilibrium steady state factorizes about any second-class particle, which implies factorization in the one-component system about the (random) shock position. It also exhibits several other interesting features, including long-range correlations in the limit of zero density of the second-class particles. The solution also shows that a finite number of second-class particles in a uniform background of first-class particles form a weakly bound state.

Key words

Asymmetric simple exclusion process shock profiles secondclass particles Burgers equation 


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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • B. Derrida
    • 1
  • S. A. Janowsky
    • 2
  • J. L. Lebowitz
    • 4
  • E. R. Speer
    • 2
  1. 1.Service de Physique ThéoriqueCEN SaclayGif-sur-YvetteFrance
  2. 2.Department of MathematicsRutgers UniversityNew Brunswick
  3. 3.Department of MathematicsUniversity of TexasAustin
  4. 4.Departments of Mathematics and PhysicsRutgers UniversityNew Brunswick

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