2006/12/31 by O. Golinelli, O Golinelli, K. Mallick +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Random Matrices and Applications #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/40/22/003
published as J. Phys. A: Math. Theor. 40 (2007) 5795-5812 · 26 pages, 1 figure; v2: published version with minor changes, revised title, 4 refs added
openalex publication_date 2007/05/14 · arxiv created 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.