2013/11/30 by Chihiro Matsui
Mathematics · Physics and Astronomy · #Algorithm #Asymmetric simple exclusion process #Mathematics #Physics #Random Matrices and Applications #Simple (philosophy) #State (computer science) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/s10955-014-1121-9
published as J. Stat. Phys. 158, 158-191 (2015) · 41pages, 10 figures; explicit forms of the fused Temperley-Lieb generators are added; J. Stat. Phys. (2014)
openalex publication_date 2014/09/26 · arxiv created 2014/12/08 · arxiv updated 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.