Two-Species Asymmetric Simple Exclusion Process with Open Boundaries

Abstract

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 polynomials, we arrive at integral formulae for the partition function and the n-point functions. We examine the thermodynamic limit and find three phases: the low-density phase, the high-density phase and the maximal current phase.

17 pages, 2 figures

References in corpus (9)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials
• Spatial Particle Condensation for an Exclusion Process on a Ring
• Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System
• Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle
• Correlation Function of Asymmetric Simple Exclusion Process with Open Boundaries

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• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Combinatorics of the two-species ASEP and Koornwinder moments
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Integrable boundary conditions for multi-species ASEP
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Combinatorial mappings of exclusion processes
• Tableaux combinatorics of the two-species PASEP
• Matrix product solution to multi-species ASEP with open boundaries
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• Matrix ansatz and combinatorics of the $k$-species PASEP
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Approximating the stationary distribution of the ASEP with open boundaries
• KPZ fluctuations in finite volume
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• Matrix Product representation of the stationary state of the open Zero Range Process
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• Inhomogeneous discrete-time exclusion processes
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Synchronized shocks in an inhomogeneous exclusion process
• Integrability in out-of-equilibrium systems
• Matrix product solution of the stationary states of two-species open zero range processes