Quantum integrable models of interacting bosons and classical \(r\)-matrices with spectral parameters

DOI10.1016/J.GEOMPHYS.2015.07.015zbMath1326.81280OpenAlexW899595894MaRDI QIDQ490970

T. V. Skrypnik

Publication date: 21 August 2015

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2015.07.015

zbMATH Keywords

quantum integrable systemsclassical \(r\)-matricesreductive Lie algebras

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Many-body theory; quantum Hall effect (81V70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (6)

``Generalized algebraic Bethe ansatz, Gaudin-type models and \(Z_{p}\)-graded classical \(r\)-matrices ⋮ Reductions in finite-dimensional integrable systems and special points of classical r-matrices ⋮ Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field ⋮ ``Twisted rational \(r\)-matrices and the algebraic Bethe ansatz: applications to generalized Gaudin models, Bose-Hubbard dimers, and Jaynes-Cummings-Dicke-type models ⋮ Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model ⋮ Z₂-graded classicalr-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

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