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

DOI10.1063/1.3205453zbMath1283.81084OpenAlexW1993569133MaRDI QIDQ3583662

T. V. Skrypnik

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3205453

zbMATH Keywords

symmetry algebrasJaynes-Cummings modelDicke modelintegrable generalizationsintegrable quantum Hamiltonian

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Quantum optics (81V80) Groups and algebras in quantum theory and relations with integrable systems (81R12) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

Related Items (12)

Reductions in finite-dimensional integrable systems and special points of classical r-matrices ⋮ Gaudin-type models, non-skew-symmetric classical \(r\)-matrices and nested Bethe ansatz ⋮ Extending third quantization with commuting observables: a dissipative spin-boson model ⋮ Modifiedn-level,n− 1-mode Tavis–Cummings model and algebraic Bethe ansatz ⋮ Rational r-matrices, higher rank Lie algebras and integrable proton-neutron BCS models ⋮ An integrable (classical and quantum) four-wave mixing Hamiltonian system ⋮ Quantum integrable models of interacting bosons and classical \(r\)-matrices with spectral parameters ⋮ Integrability and correspondence of classical and quantum non-linear three-mode systems ⋮ ``Twisted rational \(r\)-matrices and the algebraic Bethe ansatz: applications to generalized Gaudin models, Bose-Hubbard dimers, and Jaynes-Cummings-Dicke-type models ⋮ General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters ⋮ Integrable equations for the model with \(N\) sources and \(n-1\) modes ⋮ Z₂-graded classicalr-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

Cites Work

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• Generalizedn-level Jaynes–Cummings and Dicke models, classical rationalr-matrices and algebraic Bethe ansatz
• On quantum integrable models related to nonlinear quantum optics. An algebraic Bethe ansatz approach
• Coherence in Spontaneous Radiation Processes

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