Perturbation series for Jacobi matrices and the quantum Rabi model

IF 1 Q1 MATHEMATICS
Mirna Charif, Lech Zielinski
{"title":"Perturbation series for Jacobi matrices and the quantum Rabi model","authors":"Mirna Charif, Lech Zielinski","doi":"10.7494/OPMATH.2021.41.3.301","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Opuscula Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7494/OPMATH.2021.41.3.301","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

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.
Jacobi矩阵的摄动级数和量子Rabi模型
研究了一类具有离散谱的无界自伴随算子的无限三对角矩阵的特征值摄动。特别地,我们得到了微扰级数收敛半径的显式估计和包括共振情况的量子拉比模型的误差估计。为了评价Jaynes和Cummings的旋转波近似的质量,我们也给出了近共振系数的表达式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信