Exact solution of the totally asymmetric simple exclusion process: Shock profiles |
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Authors: | B. Derrida S. A. Janowsky J. L. Lebowitz E. R. Speer |
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Affiliation: | (1) Service de Physique Théorique, CEN Saclay, F-91191 Gif-sur-Yvette, France;(2) Department of Mathematics, Rutgers University, 08903 New Brunswick, New Jersey;(3) Present address: Department of Mathematics, University of Texas, Austin, Texas;(4) Departments of Mathematics and Physics, Rutgers University, New Brunswick, New Jersey |
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Abstract: | 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. |
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Keywords: | Asymmetric simple exclusion process shock profiles secondclass particles Burgers equation |
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