2015/03/04 by Federico Zullo · 4 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Chain (unit) #Integrable system #Monodromy #Nonlinear Waves and Solitons #Operator (biology) #Property (philosophy) #Quantum #TRACE (psycholinguistics) #Yang–Baxter equation #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/12/125205
published in Journal of Physics A Mathematical and Theoretical 48(12), 125205 (Institute of Physics) · 16 pages
openalex publication_date 2015/03/04 · arxiv created 2015/08/07 · arxiv updated 2015/08/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct the Baxter operator and the corresponding Baxter equation for a quantum version of the Ablowitz–Ladik model. The result is achieved in two different ways: by using the well-known Bethe ansatz technique and by looking at the quantum analogue of the classical Bäcklund transformations. General results about integrable models governed by the same r -matrix algebra will be given. Baxter's equation comes out to be a q-difference equation involving both the trace and the quantum determinant of the monodromy matrix. The spectrality property of the classical Bäcklund transformations gives a trace formula representing the classical analogue of Baxter's equation. A q-integral representation of the Baxter operator is discussed.