Elliptic three-boson system, “two-level three-mode” JCD-type models and non-skew-symmetric classical r-matrices |
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Authors: | T. Skrypnyk |
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Affiliation: | a Universita degli Studi di Milano-Bicocca, via Roberto Cozzi 53, 20125 Milano, Italy b Bogoliubov Institute for Theoretical Physics, Metrologichna st. 14-b, 03143 Kiev, Ukraine |
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Abstract: | Using the technique of the classical r-matrices and quantum Lax operators we construct the most general form of quantum integrable multi-boson and spin-multi-boson models associated with linear Lax algebras and sl(2)⊗sl(2)-valued classical non-dynamical r-matrices with spectral parameters. We consider example of non-skew-symmetric elliptic r-matrix and explicitly obtain one-, two- and three-boson integrable models and the corresponding one-, two- and three-mode two-level Jaynes-Cummings-Dicke-type models. We show that integrable “elliptic” two-level one-mode Jaynes-Cummings-Dicke Hamiltonian is hermitian and contains both rotating and counter-rotating terms. |
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Keywords: | Integrable systems Classical r-matrices Algebraic Bethe ansatz |
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