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Title: General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters

Abstract

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.

Authors:
 [1]
  1. Universita degli Studi di Milano-Bicocca, via Roberto Cozzi, 53, 20125 Milano, Italy and Bogoliubov Institute for Theoretical Physics, Metrologichna st.14-b, 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., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua. General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters. United States: N. p., 2015. Web. doi:10.1063/1.4907980.
Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua. General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters. United States. doi:10.1063/1.4907980.
Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua. Sun . "General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters". United States. doi:10.1063/1.4907980.
@article{osti_22403115,
title = {General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters},
author = {Skrypnyk, T., E-mail: taras.skrypnyk@unimib.it, E-mail: tskrypnyk@imath.kiev.ua},
abstractNote = {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.},
doi = {10.1063/1.4907980},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = {Sun Feb 15 00:00:00 EST 2015},
month = {Sun Feb 15 00:00:00 EST 2015}
}