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Integrability and superintegrability of the generalized n-level many-mode Jaynes–Cummings and Dicke models

J. Math. Phys. 50, 103523 (2009); doi:10.1063/1.3205453

Published 8 October 2009

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T. Skrypnyk
International School for Advanced Studies, via Beirut 2-4, 34014 Trieste, Italy and Bogoliubov Institute for Theoretical Physics, Metrologichna st.14-b, Kiev 03143, Ukraine
We analyze symmetries of the integrable generalizations of Jaynes–Cummings and Dicke models associated with simple Lie algebras [fraktur g] and their reductive subalgebras [fraktur g]K [T. Skrypnyk, “Generalized n-level Jaynes-Cummings and Dicke models, classical rational r-matrices and nested Bethe ansatz,” J. Phys. A: Math. Theor. 41, 475202 (2008)]. We show that their symmetry algebras contain commutative subalgebras isomorphic to the Cartan subalgebras of [fraktur g], which can be added to the commutative algebras of quantum integrals generated with the help of the quantum Lax operators. We diagonalize additional commuting integrals and constructed with their help the most general integrable quantum Hamiltonian of the generalized n-level many-mode Jaynes–Cummings and Dicke-type models using nested algebraic Bethe ansatz. ©2009 American Institute of Physics
History: Received 17 January 2009; accepted 24 July 2009; published 8 October 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/103523/1
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0022-2488 (print)   1089-7658 (online)
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