Algebraic Bethe Ansatz for the two species ASEP with different hopping rates

Abstract

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans. We present also formulas for the total velocity of particles of a given type and their limit for large size of the system and finite densities of the particles.

arXiv comment14 pages

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• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Open two-species exclusion processes with integrable boundaries
• On the asymmetric simple exclusion process with multiple species
• Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
• Matrix product solution to an inhomogeneous multi-species TASEP
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Equivalent T-Q relations and exact results for the open TASEP
• Generalized matrix Ansatz in the multispecies exclusion process - partially asymmetric case
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Hydrodynamic behavior of the 2-TASEP
• A new braid-like algebra for Baxterisation
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Limiting current distribution for a two species asymmetric exclusion process
• KPZ fluctuations in finite volume
• Integrability of two-species partially asymmetric exclusion processes
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• Inhomogenous Multispecies TASEP on a ring with spectral parameters
• One-dimensional Particle Processes with Acceleration/Braking Asymmetry
• Current fluctuations for the second class particle : joint statistics