Connected Operators for the Totally Asymmetric Exclusion Process

Abstract

We fully elucidate the structure of the hierarchy of the connected operators that commute with the Markov matrix of the Totally Asymmetric Exclusion Process (TASEP). We prove for the connected operators a combinatorial formula that was conjectured in a previous work. Our derivation is purely algebraic and relies on the algebra generated by the local jump operators involved in the TASEP. Keywords: Non-Equilibrium Statistical Mechanics, ASEP, Exact Results, Algebraic Bethe Ansatz.

10 pages

References in corpus (5)

• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• The asymmetric exclusion model with sequential update
• An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process

Cited by in corpus (3)

• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Cumulants of the current in the weakly asymmetric exclusion process
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states