Multi-state asymmetric simple exclusion processes

Abstract

It is known that the Markov matrix of the asymmetric simple exclusion process (ASEP) is invariant under the Uq(sl2) algebra. This is the result of the fact that the Markov matrix of the ASEP coincides with the generator of the Temperley-Lieb (TL) algebra, the dual algebra of the Uq(sl2) algebra. Various types of algebraic extensions have been considered for the ASEP. In this paper, we considered the multi-state extension of the ASEP, by allowing more than two particles to occupy the same box. We constructed the Markov matrix by dimensionally extending the TL generators and derived explicit forms of the particle densities and the currents on the steady states. Then we showed how decay lengths differ from the original two-state ASEP under the closed boundary conditions.

41pages, 10 figures; explicit forms of the fused Temperley-Lieb generators are added; J. Stat. Phys. (2014)

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Cited by in corpus (7)

• Asymmetric stochastic transport models with ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ symmetry
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Stochastic Fusion of Interacting Particle Systems and Duality Functions
• A generalized Asymmetric Exclusion Process with $U_q({\mathfrak{sl}}_2)$ stochastic duality
• KPZ fluctuations in finite volume
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries