Family of Commuting Operators for the Totally Asymmetric Exclusion Process

Abstract

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of operators (called generalized hamiltonians) that commute with the Markov operator. The transfer matrix, which is the generating function of these operators, is shown to represent a discrete Markov process with long-range jumps. We give a general combinatorial formula for the connected hamiltonians obtained by taking the logarithm of the transfer matrix. This formula is proved using a symbolic calculation program for the first ten connected operators. Keywords: ASEP, Algebraic Bethe Ansatz. Pacs numbers: 02.30.Ik, 02.50.-r, 75.10.Pq.

arXiv comment26 pages, 1 figure; v2: published version with minor changes, revised title, 4 refs added

References in corpus (13)

• Exact Large Deviation Function in the Asymmetric Exclusion Process
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• The asymmetric exclusion model with sequential update
• A Spin Chain Primer
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• An Exactly Solvable Anisotropic Directed Percolation Model in Three Dimensions
• Spectral Degeneracies in the Totally Asymmetric Exclusion Process
• Hidden symmetries in the asymmetric exclusion process

Cited by in corpus (6)

• 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
• Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
• KPZ fluctuations in finite volume
• Connected Operators for the Totally Asymmetric Exclusion Process