Bethe ansatz solution for a defect particle in the asymmetric exclusion process

B Derrida*, MR Evans

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)4833-4850
Number of pages18
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number26
Publication statusPublished - 2 Jul 1999

Keywords

  • DRIVEN DIFFUSIVE SYSTEMS
  • STOCHASTIC-MODELS
  • QUADRATIC ALGEBRAS
  • SHOCK FLUCTUATIONS
  • GROWTH
  • BOUNDARIES

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