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

2003/12/18 by Masaru Uchiyama, Tomohiro Sasamoto, Miki Wadati · 4 citations
Mathematics · Physics and Astronomy · #Askey–Wilson polynomials #Asymmetric simple exclusion process #Boundary (topology) #Combinatorics #Difference polynomials #Macdonald polynomials #Mathematical analysis #Mathematical physics #Mathematics #Orthogonal polynomials #Partition (number theory) #Partition function (quantum field theory) #Phase (matter) #Phase diagram #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Simple (philosophy) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/0305-4470/37/18/006

published as J. Phys. A: Math. Gen. 37 (2004) 4985-5002 · 21 pages, 2 figures

arxiv created 2003/12/18 · openalex publication_date 2004/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• One-dimensional partially asymmetric simple exclusion process on a ring with a defect particle
• Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process
• Basic Hypergeometric Series
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

Cited by

• Integrability in out-of-equilibrium systems
• Tree structures for the current fluctuations in the exclusion process
• Askey–Wilson polynomials, quadratic harnesses and martingales
• Active gating: rocking diffusion channels