Perturbation series for Jacobi matrices and the quantum Rabi model

Opuscula Mathematica

article

Mirna Charif¹  Lech Zielinski (corresponding author)² 

[1] Lebanese University, Faculty of Sciences, Department of Mathematics;Université du Littoral Côte d’Opale, Laboratoire de Mathématiques Pures et Appliquées

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

DOI  :  10.7494/OpMath.2021.41.3.301

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC