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Exact Results for the Asymmetric Simple Exclusion Process with a Blockage

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.