General integrable nlevel, manymode JanesCummingsDicke models and classical rmatrices with spectral parameters
Abstract
Using the technique of classical rmatrices and quantum Lax operators, we construct the most general form of the quantum integrable “nlevel, manymode” spinboson JaynesCummingsDicketype hamiltonians describing an interaction of a molecule of N nlevel atoms with many modes of electromagnetic field and containing, in general, additional nonlinear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spinboson 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 rmatrices and construct the corresponding algebra of quantum integrals. We consider in detail three classes of nonskewsymmetric classical rmatrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and JaynesCummingsDicketype hamiltonians depending on the considered rmatrix.
 Authors:
 Universita degli Studi di MilanoBicocca, via Roberto Cozzi, 53, 20125 Milano, Italy and Bogoliubov Institute for Theoretical Physics, Metrologichna st.14b, 03143 Kiev (Ukraine)
 Publication Date:
 OSTI Identifier:
 22403115
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTROMAGNETIC FIELDS; HAMILTONIANS; INTEGRAL CALCULUS; LAX THEOREM; NONLINEAR PROBLEMS; R MATRIX; SYMMETRY
Citation Formats
Skrypnyk, T., Email: taras.skrypnyk@unimib.it, Email: tskrypnyk@imath.kiev.ua. General integrable nlevel, manymode JanesCummingsDicke models and classical rmatrices with spectral parameters. United States: N. p., 2015.
Web. doi:10.1063/1.4907980.
Skrypnyk, T., Email: taras.skrypnyk@unimib.it, Email: tskrypnyk@imath.kiev.ua. General integrable nlevel, manymode JanesCummingsDicke models and classical rmatrices with spectral parameters. United States. doi:10.1063/1.4907980.
Skrypnyk, T., Email: taras.skrypnyk@unimib.it, Email: tskrypnyk@imath.kiev.ua. 2015.
"General integrable nlevel, manymode JanesCummingsDicke models and classical rmatrices with spectral parameters". United States.
doi:10.1063/1.4907980.
@article{osti_22403115,
title = {General integrable nlevel, manymode JanesCummingsDicke models and classical rmatrices with spectral parameters},
author = {Skrypnyk, T., Email: taras.skrypnyk@unimib.it, Email: tskrypnyk@imath.kiev.ua},
abstractNote = {Using the technique of classical rmatrices and quantum Lax operators, we construct the most general form of the quantum integrable “nlevel, manymode” spinboson JaynesCummingsDicketype hamiltonians describing an interaction of a molecule of N nlevel atoms with many modes of electromagnetic field and containing, in general, additional nonlinear interaction terms. We explicitly obtain the corresponding quantum Lax operators and spinboson 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 rmatrices and construct the corresponding algebra of quantum integrals. We consider in detail three classes of nonskewsymmetric classical rmatrices with spectral parameters and explicitly obtain the corresponding quantum Lax operators and JaynesCummingsDicketype hamiltonians depending on the considered rmatrix.},
doi = {10.1063/1.4907980},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = 2015,
month = 2
}

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