Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process

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.

• Publication year

  1997

• Venue

  Journal of Physics A

• Publication date

  1997-05-15

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/0305-4470/30/13/008arXiv cond-mat/9705152
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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