Exact results for the asymmetric simple exclusion process with a blockage

S. A. Janowsky; J. L. Lebowitz

doi:10.1007/BF02186831

Exact results for the asymmetric simple exclusion process with a blockage

S. A. Janowsky, J. L. Lebowitz

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126 Scopus citations

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 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 language	English (US)
Pages (from-to)	35-51
Number of pages	17
Journal	Journal of Statistical Physics
Volume	77
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02186831
State	Published - Oct 1994

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Asymmetric simple exclusion process
series expansion
stochastic particle systems

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10.1007/BF02186831

Cite this

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title = "Exact results for the asymmetric simple exclusion process with a blockage",

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 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. Pad{\'e} 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.",

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T1 - Exact results for the asymmetric simple exclusion process with a blockage

AU - Janowsky, S. A.

AU - Lebowitz, J. L.

PY - 1994/10

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N2 - 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.

AB - 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.

KW - Asymmetric simple exclusion process

KW - series expansion

KW - stochastic particle systems

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Exact results for the asymmetric simple exclusion process with a blockage

Abstract

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