带洞域上的磁性诺依曼拉普拉卡方

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2023-12-30 DOI:10.1016/s0034-4877(23)00079-4

Diana Barseghyan, Baruch Schneider, Swanhild Bernstein

{"title":"带洞域上的磁性诺依曼拉普拉卡方","authors":"Diana Barseghyan, Baruch Schneider, Swanhild Bernstein","doi":"10.1016/s0034-4877(23)00079-4","DOIUrl":null,"url":null,"abstract":"<p>In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.</p>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Magnetic Neumann Laplacian on a domain with a hole\",\"authors\":\"Diana Barseghyan, Baruch Schneider, Swanhild Bernstein\",\"doi\":\"10.1016/s0034-4877(23)00079-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.</p>\",\"PeriodicalId\":49630,\"journal\":{\"name\":\"Reports on Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1016/s0034-4877(23)00079-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1016/s0034-4877(23)00079-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们研究了带有小洞的域上的磁性诺依曼拉普拉斯。我们的注意力集中在洞的描述上，因为洞不会使频谱发生巨大变化。此外，我们还证明了磁性诺伊曼拉普拉斯的谱在豪斯多夫距离的意义上收敛于定义在未扰动域上的原始算子的谱。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Magnetic Neumann Laplacian on a domain with a hole

In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.

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

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.