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

IF 0.7 4区 数学 Q2 MATHEMATICS St Petersburg Mathematical Journal 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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来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
审稿时长
>12 weeks
期刊介绍: This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
期刊最新文献
Shape, velocity, and exact controllability for the wave equation on a graph with cycle On Kitaev’s determinant formula Resolvent stochastic processes Complete nonselfadjointness for Schrödinger operators on the semi-axis Behavior of large eigenvalues for the two-photon asymmetric quantum Rabi model
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