Perturbation series for Jacobi matrices and the quantum Rabi model

DOI10.7494/OpMath.2021.41.3.301zbMath1469.81019OpenAlexW3156767494MaRDI QIDQ5004076

Mirna Charif, Lech Zielinski

Publication date: 30 July 2021

Published in: Opuscula Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7494/opmath.2021.41.3.301

zbMATH Keywords

perturbation seriesJacobi matrixrotating wave approximationunbounded self-adjoint operatorsquantum Rabi modelquasi-degenerate eigenvalue perturbation

Mathematics Subject Classification ID

Convergence and divergence of series and sequences of functions (40A30) Eigenvalues, singular values, and eigenvectors (15A18) Quantum optics (81V80) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Resonance in context of PDEs (35B34) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Cites Work

• Perturbation theory for linear operators.
• The quantum Rabi model: solution and dynamics
• Semi-classical and quantum Rabi models: in celebration of 80 years
• Infinite Jacobi Matrices with Unbounded Entries: Asymptotics of Eigenvalues and the Transformation Operator Approach
• On the spectrum of the quantum Rabi model
• On the Process of Space Quantization
• Space Quantization in a Gyrating Magnetic Field
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