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Behavior of large eigenvalues for the two-photon asymmetric quantum Rabi model
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by A. Boutet de Monvel, M. Charif and L. Zielinski

St. Petersburg Math. J. 35 (2024), 61-82

DOI: https://doi.org/10.1090/spmj/1793

Published electronically: April 12, 2024

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Abstract:

The asymptotic behavior of large eigenvalues is studied for the two-photon quantum Rabi model with a finite bias. It is proved that the spectrum of this Hamiltonian model consists of two eigenvalue sequences $\lbrace E_n^+\rbrace _{n=0}^{\infty }$, $\lbrace E_n^-\rbrace _{n=0}^{\infty }$, and their large $n$ asymptotic behavior with error term $\operatorname {O}(n^{-1/2})$ is described. The principal tool is the method of near-similarity of operators introduced by G. V. Rozenblum and developed in works of J. Janas, S. Naboko, and E. A. Yanovich (Tur).

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