Perturbation series for Jacobi matrices and the quantum Rabi model

• Autorzy: Charif Mirna , Zielinski Lech

Identyfikatory

DOI

10.7494/OpMath.2021.41.3.301

• Języki publikacji: EN

Abstrakty

EN

We investigate eigenvalue perturbations for a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. In particular we obtain explicit estimates for the convergence radius of the perturbation series and error estimates for the Quantum Rabi Model including the resonance case. We also give expressions for coefficients near resonance in order to evaluate the quality of the rotating wave approximation due to Jaynes and Cummings. .

Słowa kluczowe

EN

Jacobi matrix; unbounded self-adjoint operators; quasi-degenerate eigenvalue perturbation; perturbation series; quantum Rabi model; rotating wave approximation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 3
• Strony: 303--333
• Opis fizyczny: BIbliogr. 23 poz,

Twórcy

autor

Charif Mirna

• Universite du Littoral Cote d’Opale Laboratoire de Mathematiques Pures et Appliquees Joseph Liouville EA 2597 F-62228 Calais, France
• Lebanese University Faculty of Sciences Department of Mathematics P.O. Box 826 Tripoli, Lebanon

• https://orcid.org/0000-0002-4403-1453

autor

Zielinski Lech

• Universite du Littoral Cote d’Opale Laboratoire de Mathematiques Pures et Appliquees Joseph Liouville EA 2597 F-62228 Calais, France

• https://orcid.org/0000-0002-7314-7586

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).