Symmetric simple exclusion process with free boundaries

Two-Species Asymmetric Simple Exclusion Process with Open Boundaries

We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical quantities are calculated through an explicit representation for the matrix products. By making full use of the relation with the continuous big q-Hermite polynomi...

Correlation Function of Asymmetric Simple Exclusion Process with Open Boundaries

We investigate the correlation functions of the one-dimensional Asymmetric Simple Exclusion Process (ASEP) with open boundaries. The conditions for the boundaries are made most general. The correlation function is expressed in a multifold integral whose behavior we study in detail. We present a phase diagram of the correlation length. For the case the correlation length diverges, we further giv...

Symmetric Simple Exclusion Process: Regularity of the Self Diffusion Coefficient

Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation...

Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

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 AskeyWilson polynomials. The partition function and the n-point functions are obtained in the integral form with four boundary parameters. The thermodynamic cu...