Matrix product solution of the multispecies partially asymmetric exclusion process

Abstract

We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a system of N species are defined recursively in terms of the matrices for a system of N-1 species. A complete proof is given, based on the quadratic relations verified by these matrices. This matrix product construction is interpreted in terms of the action of a transfer matrix.

27 pages, 3 figures

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• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Some Exact Results for the Exclusion Process
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• An Inhomogeneous Multispecies TASEP on a Ring
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Recursive structures in the multispecies TASEP
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Integrable dissipative exclusion process: Correlation functions and physical properties
• Exact results for an asymmetric annihilation process with open boundaries
• Quantum algebra symmetry of the ASEP with second-class particles
• Phase diagram of the ABC model with nonconserving processes
• Combinatorial mappings of exclusion processes
• Multi-state asymmetric simple exclusion processes
• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• Two-species active transport along cylindrical biofilaments is limited by emergent topological hindrance
• Inhomogeneous generalization of multispecies totally asymmetric zero range process
• Limiting current distribution for a two species asymmetric exclusion process
• Multiline queues with spectral parameters
• KPZ fluctuations in finite volume
• Modified Macdonald polynomials and the multispecies zero range process: II
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• General limit distributions for sums of random variables with a matrix product representation
• Density and current profiles in $U_q(A_2^{(1)})$ zero range process
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• Transfer matrices for the totally asymmetric exclusion process
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion
• Correlations in the multispecies PASEP on a ring
• Distribution of a second-class particle's position in the two-species ASEP with a special initial configuration