Using the technique of classical r-matrices and quantum Lax operators, we construct the most general form of the quantum integrable "n-level, many-mode" spin-boson Jaynes-Cummings-Dicke-type hamiltonians describing an interaction of a molecule of N n-level atoms with many modes of electromagnetic field and containing, in general, additional non-linear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spin-boson analogs of the generalized Gaudin hamiltonians and prove their quantum commutativity. We investigate symmetries of the obtained models that are associated with the geometric symmetries of the classical r-matrices and construct the corresponding algebra of quantum integrals. We consider in detail three classes of non-skew-symmetric classical r-matrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and Jaynes-Cummings-Dicke-type hamiltonians depending on the considered r-matrix.
SKRYPNYK, T. (2015). General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters. JOURNAL OF MATHEMATICAL PHYSICS, 56(2) [10.1063/1.4907980].
Citazione: | SKRYPNYK, T. (2015). General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters. JOURNAL OF MATHEMATICAL PHYSICS, 56(2) [10.1063/1.4907980]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters | |
Autori: | SKRYPNYK, T | |
Autori: | SKRYPNYK, TARAS (Primo) (Corresponding) | |
Data di pubblicazione: | 2015 | |
Lingua: | English | |
Rivista: | JOURNAL OF MATHEMATICAL PHYSICS | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1063/1.4907980 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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