Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and tha...

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Bibliographic Details
Published in:Physical review letters 2004-07, Vol.93 (4), p.040602.1-040602.4, Article 040602
Main Authors: DEPKEN, Martin, STINCHCOMBE, Robin
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
Mathematical methods in physics
Physics
Probability theory, stochastic processes, and statistics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.93.040602