K Mallick and S Sandow 1997 J. Phys. A: Math. Gen. 30 4513 doi:10.1088/0305-4470/30/13/008
Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process
K Mallick
,
and S Sandow§
We study the one-dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite-dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.
- PACS
- MSC
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15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)
17A45 Quadratic algebras (but not quadratic Jordan algebras)
- Subjects
- Dates
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Issue 13 (7 July 1997)
Received 18 February 1997, in final form 28 April 1997
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Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process
K Mallick and S Sandow 1997 J. Phys. A: Math. Gen. 30 4513
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