论有界区间内狄拉克算子的特征值个数

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Annales Henri Poincaré Pub Date : 2024-04-06 DOI:10.1007/s00023-024-01431-4

Jason Holt, Oleg Safronov

{"title":"论有界区间内狄拉克算子的特征值个数","authors":"Jason Holt, Oleg Safronov","doi":"10.1007/s00023-024-01431-4","DOIUrl":null,"url":null,"abstract":"Let \\(H_0\\) be the free Dirac operator and \\(V \\geqslant 0\\) be a positive potential. We study the discrete spectrum of \\(H(\\alpha )=H_0-\\alpha V\\) in the interval \\((-1,1)\\) for large values of the coupling constant \\(\\alpha >0\\). In particular, we obtain an asymptotic formula for the number of eigenvalues of \\(H(\\alpha )\\) situated in a bounded interval \\([\\lambda ,\\mu )\\) as \\(\\alpha \\rightarrow \\infty \\).\n","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"2 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Number of Eigenvalues of the Dirac Operator in a Bounded Interval\",\"authors\":\"Jason Holt, Oleg Safronov\",\"doi\":\"10.1007/s00023-024-01431-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\(H_0\\\\) be the free Dirac operator and \\\\(V \\\\geqslant 0\\\\) be a positive potential. We study the discrete spectrum of \\\\(H(\\\\alpha )=H_0-\\\\alpha V\\\\) in the interval \\\\((-1,1)\\\\) for large values of the coupling constant \\\\(\\\\alpha >0\\\\). In particular, we obtain an asymptotic formula for the number of eigenvalues of \\\\(H(\\\\alpha )\\\\) situated in a bounded interval \\\\([\\\\lambda ,\\\\mu )\\\\) as \\\\(\\\\alpha \\\\rightarrow \\\\infty \\\\).\\n\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://doi.org/10.1007/s00023-024-01431-4\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01431-4","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

让 \(H_0\) 是自由狄拉克算子，\(V \geqslant 0\) 是一个正电势。我们研究了耦合常数\(\alpha >0\)的大值时\((-1,1)\)区间内\(H(\alpha )=H_0-\alpha V\) 的离散谱。特别是，我们得到了位于有界区间（[\lambda ,\mu)）内的\(H(\alpha )的特征值的数量的渐近公式，即\(\alpha \右箭头 \左箭头)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On the Number of Eigenvalues of the Dirac Operator in a Bounded Interval

Let \(H_0\) be the free Dirac operator and \(V \geqslant 0\) be a positive potential. We study the discrete spectrum of \(H(\alpha )=H_0-\alpha V\) in the interval \((-1,1)\) for large values of the coupling constant \(\alpha >0\). In particular, we obtain an asymptotic formula for the number of eigenvalues of \(H(\alpha )\) situated in a bounded interval \([\lambda ,\mu )\) as \(\alpha \rightarrow \infty \).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.