Behavior of large eigenvalues for the two-photon asymmetric quantum Rabi model

Pub Date : 2024-04-12 DOI:10.1090/spmj/1793

A. Boutet de Monvel, M. Charif, L. Zielinski

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引用次数: 0

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 { E n + } n = 0 ∞ \lbrace E_n^+\rbrace _{n=0}^{\infty } , { E n − } n = 0 ∞ \lbrace E_n^-\rbrace _{n=0}^{\infty } , and their large n n asymptotic behavior with error term O ⁡ ( n − 1 / 2 ) \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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双光子不对称量子拉比模型的大特征值行为

研究了具有有限偏置的双光子量子拉比模型的大特征值渐近行为。研究证明，该哈密顿模型的谱由两个特征值序列组成 { E n + } n = 0 ∞ \lbrace E_n^+\rbrace _{n=0}^{\infty } ， { E n - } n = 0 ∞ \lbrace E_n^+\rbrace _{n=0}^{\infty } 。 { E n - } n = 0 ∞ \lbrace E_n^-\rbrace _{n=0}^{\infty } ，以及它们的大 n n 渐近线。描述了它们的大 n n 渐近行为，误差项为 O ( n - 1 / 2 ) \operatorname {O}(n^{-1/2}) 。主要工具是由 G. V. Rozenblum 引入并在 J. Janas、S. Naboko 和 E. A. Yanovich (Tur) 的著作中发展的算子近似方法。

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