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Derivation of a matrix product representation for the asymmetric exclusion process from the algebraic Bethe ansatz

Journal of Physics A: Mathematical and General, ISSN: 0305-4470, Vol: 39, Issue: 34, Page: 10647-10658
2006
  • 36
    Citations
  • 0
    Usage
  • 6
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    36
    • Citation Indexes
      36
  • Captures
    6

Article Description

We derive, using the algebraic Bethe ansatz, a generalized matrix product ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this matrix product ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they generate a quadratic algebra. Our construction provides explicit finite-dimensional representations for the generators of this algebra. © 2006 IOP Publishing Ltd.

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