Exact solution of an exclusion process with three classes of particles and vacancies

Abstract

We present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies. Using a matrix product Ansatz, we find explicit expressions for the weights of the configurations in the stationary state. The solution involves tensor products of quadratic algebras.

18 pages, no figures, LaTeX

References in corpus (15)

• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• Exact solution of a cellular automaton for traffic
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• A multi-species asymmetric simple exclusion process and its relation to traffic flow
• On Matrix Product Ground States for Reaction-Diffusion Models
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
• The asymmetric exclusion model with sequential update
• Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras
• Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
• N-species stochastic models with boundaries and quadratic algebras
• Exact results for one dimensional stochastic cellular automata for different types of updates
• The asymmetric exclusion process: Comparison of update procedures
• Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update

Cited by in corpus (30)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Stationary distributions of multi-type totally asymmetric exclusion processes
• Matrix representation of the stationary measure for the multispecies TASEP
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Some Exact Results for the Exclusion Process
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Current Fluctuations in the exclusion process and Bethe Ansatz
• One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle
• Generalized Exclusion Processes: Transport Coefficients
• Open two-species exclusion processes with integrable boundaries
• Disordered exclusion process revisited: some exact results in the low-current regime
• Recursive structures in the multispecies TASEP
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Stochastic Dynamics of Discrete Curves and Multi-type Exclusion Processes
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• An interacting spin flip model for one-dimensional proton conduction
• On Matrix Product States for Periodic Boundary Conditions
• Limiting current distribution for a two species asymmetric exclusion process
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• KPZ fluctuations in finite volume
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Matrix Product States for Interacting Particles without Hardcore Constraints
• Transfer matrices for the totally asymmetric exclusion process
• Multi species asymmetric simple exclusion process with impurity activated flips
• Asymmetric exclusion model with several kinds of impurities
• Exact determination of the phase structure of the p-species asymmetric exclusion process
• Some general features of matrix product states in stochastic systems