Oscillatory Behavior of Large Eigenvalues in Quantum Rabi Models-Reference-Cited by-同舟云学术

Oscillatory Behavior of Large Eigenvalues in Quantum Rabi Models

Published:2019-01-24 Issue:7 Volume:2021 Page:5155-5213
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Boutet de Monvel Anne¹,Zielinski Lech²

Affiliation:

1. Institut de Mathématiques de Jussieu-PRG, Université Paris Diderot, Bâtiment Sophie Germain, case, Paris Cedex 13, France

2. Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral Côte d’Opale, Calais, France

Abstract

Abstract We investigate the large $n$ asymptotics of the $n$-th eigenvalue for a class of unbounded self-adjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the 1st three terms of the asymptotics that determine the parameters of the model. This paper is based on our previous paper [5] that it completes and improves.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/7/5155/36871999/rny294.pdf

Reference21 articles.

1. The asymptotic behavior of eigenvalues of a modified Jaynes–Cummings model;Boutet de Monvel;Asymptot. Anal.,2006

2. Eigenvalue asymptotics for Jaynes–Cummings type models without modulations;Boutet de Monvel,2008

3. Explicit error estimates for eigenvalues of some unbounded Jacobi matrices;Boutet de Monvel,2012

4. Asymptotic behavior of large eigenvalues of a modified Jaynes–Cummings model;Boutet de Monvel,2014

5. Asymptotic behavior of large eigenvalues for Jaynes–Cummings type models;Boutet de Monvel;J. Spectr. Theory,2017

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Spacing distribution for quantum Rabi models ^*;Journal of Physics A: Mathematical and Theoretical;2024-07-04

2. The quantum Rabi model: towards Braak’s conjecture;Journal of Physics A: Mathematical and Theoretical;2024-07-01

3. Behavior of large eigenvalues for the two-photon asymmetric quantum Rabi model;St. Petersburg Mathematical Journal;2024-04-12

4. Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model;Comptes Rendus. Mathématique;2023-12-21

5. Behaviour of large eigenvalues for the asymmetric quantum Rabi model;Asymptotic Analysis;2023-11-15