Uchiyama, Masaru; Sasamoto, Tomohiro; Wadati, Miki Asymmetric simple exclusion process with open boundaries and Askey-Wilson polynomials. (English) Zbl 1047.82019 J. Phys. A, Math. Gen. 37, No. 18, 4985-5002 (2004). Summary: 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. Cited in 2 ReviewsCited in 42 Documents MSC: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics PDFBibTeX XMLCite \textit{M. Uchiyama} et al., J. Phys. A, Math. Gen. 37, No. 18, 4985--5002 (2004; Zbl 1047.82019) Full Text: DOI arXiv