2020/06/02 by Guido Magnano, Universit&, Taras Skrypnyk +3
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chemistry #Chromatography #Degenerate energy levels #Geometry #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Separation of variables #Spin (aerodynamics) #Thermodynamics #Twist #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.3842/sigma.2020.047
published as SIGMA 16 (2020), 047, 27 pages
arxiv created 2020/06/02 · openalex publication_date 2020/06/02 · arxiv updated 2020/06/03 · openalex created_date 2020/06/12 · openalex updated_date 2026/08/05
We propose a non-standard separation of variables for the classical integrable XXX and XXZ spin chains with degenerate twist matrix. We show that for the case of such twist matrices one can interchange the role of classical separating functions A(u) and B(u) and construct a new full set of separated variables, satisfying simpler equation of separation and simpler Abel equations in comparison with the standard separated variables of Sklyanin. We show that for certain cases of the twist matrices the constructed separated variables can be directly identified with action-angle coordinates.