- 93-192 Janowsky Steven A., Lebowitz Joel L.
- Exact Results for the Asymmetric Simple Exclusion Process with a Blockage
Jun 24, 93
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Abstract. 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 finite volume results serve to bound the allowed values
for the current in the infinite system. This proves the existence of a
gap in allowed density corresponding to a nonequilibrium ``phase
transition'' in the infinite system. A series expansion in r, derived
from the finite systems, is proven to be asymptotic for all sufficiently
large systems. Pade 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 a part in 10^4.