1999/01/01 by B Derrida, B. Derrida, M. R. Evans +1 · 6 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/32/26/303
Latex, 23 pages
openalex publication_date 1999/01/01 · arxiv created 1999/02/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The asymmetric exclusion process on a ring in one dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time limit behaviour of the generating function of the distance travelled by the defect particle. This allows us to recover steady state properties known from the matrix approach such as the velocity, and obtain new results such as the diffusion constant of the defect particle. In the case where the defect particle is a second-class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is Gaussian. Moreover, the variance (diffusion constant) grows as L 1/2 where L is the system size. This behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system. In the case where the defect particle produces a shock, our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by Ferrari and Fontes.