Exact results for the asymmetric simple exclusion process with a blockage

S. A. Janowsky, J. L. Lebowitz

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120 Scopus citations


We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one to r<1. Exact finitevolume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a nonequilibrium "phase transition," corresponding to an "immiscibility" gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state. A series expansion in r, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Padé approximants based on this series, which make specific assumptions about the nature of the singularity at r=1, match numerical data for the "infinite" system to 1 part in 104.

Original languageEnglish (US)
Pages (from-to)35-51
Number of pages17
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Asymmetric simple exclusion process
  • series expansion
  • stochastic particle systems


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