Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials

By M. Uchiyama, Tomohiro Sasamoto, Miki Wadati. 2003

149 citations recorded by the source corpus.

We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the Askey–Wilson polynomials. The partition function and the n-point functions are obtained in the integral form with four boundary parameters. The thermodynamic current is evaluated to confirm the conjectured phase diagram.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c31de7500ce8b289eb53e546f3dcb80ea1b3be42

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Askey--Wilson polynomials, quadratic harnesses and martingales (2008, background): “For a similar calculation see [32], Section 4.”
Formulae for Askey-Wilson moments and enumeration of staircase tableaux (2010, methodology): “Combining that theorem with the fact (due to [30]) that Zn can also be written as a constant times (x + 1)n integrated with respect to the Askey-Wilson measure yields Theorem 1.”
Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials (2009, methodology): “We then use this result together with [48] to give a combinatorial formula for the moments of the AskeyWilson polynomials.”
Nonequilibrium steady states of matrix-product form: a solver's guide (2007, background): “28) and the asymptotic analysis via a contour integral detailed in [119] is basically the same as described in Subsection 5.”