{"title":"非对称量子拉比模型大特征值的行为","authors":"Mirna Charif, Ahmad Fino, Lech Zielinski","doi":"10.3233/asy-231875","DOIUrl":null,"url":null,"abstract":"We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences (Em+)m=0∞, (Em−)m=0∞, satisfying a two-term asymptotic formula with error estimate of the form O(m−1/4), when m tends to infinity.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"43 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Behaviour of large eigenvalues for the asymmetric quantum Rabi model\",\"authors\":\"Mirna Charif, Ahmad Fino, Lech Zielinski\",\"doi\":\"10.3233/asy-231875\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences (Em+)m=0∞, (Em−)m=0∞, satisfying a two-term asymptotic formula with error estimate of the form O(m−1/4), when m tends to infinity.\",\"PeriodicalId\":55438,\"journal\":{\"name\":\"Asymptotic Analysis\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asymptotic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3233/asy-231875\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-231875","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
我们证明，当 m 趋于无穷大时，非对称量子拉比模型的频谱由两个特征值序列 (Em+)m=0∞, (Em-)m=0∞ 组成，满足两期渐近公式，误差估计为 O(m-1/4)。
Behaviour of large eigenvalues for the asymmetric quantum Rabi model
We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences (Em+)m=0∞, (Em−)m=0∞, satisfying a two-term asymptotic formula with error estimate of the form O(m−1/4), when m tends to infinity.
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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