TY  - JOUR
ID  - Charif2021
LB  - Charif2021
AU  - Charif, Mirna
AU  - Zielinski, Lech
TI  - Perturbation series for Jacobi matrices and the quantum Rabi model
ST  - Perturbation series for Jacobi matrices and the quantum Rabi model
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 3
SP  - 301
EP  - 333
DO  - https://doi.org/10.7494/OpMath.2021.41.3.301
UR  - https://doi.org/10.7494/OpMath.2021.41.3.301
AB  - 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.
KW  - Jacobi matrix
KW  - unbounded self-adjoint operators
KW  - quasi-degenerate eigenvalue perturbation
KW  - perturbation series
KW  - quantum Rabi model
KW  - rotating wave approximation
SN  - 1232-9274
ER  -