{"title":"几乎平坦的磁屏障上的磁拉普拉斯离散谱","authors":"Germán Miranda","doi":"10.1063/5.0208990","DOIUrl":null,"url":null,"abstract":"The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-Noël et al. [Bull. London Math. Soc. 56, 2529 (2024)] to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.","PeriodicalId":508452,"journal":{"name":"Journal of Mathematical Physics","volume":"44 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers\",\"authors\":\"Germán Miranda\",\"doi\":\"10.1063/5.0208990\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-Noël et al. [Bull. London Math. Soc. 56, 2529 (2024)] to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.\",\"PeriodicalId\":508452,\"journal\":{\"name\":\"Journal of Mathematical Physics\",\"volume\":\"44 5\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0208990\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0208990","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在过去几年里,人们一直在深入研究带有阶跃磁场的磁拉普拉斯。我们改编了 Bonnaillie-Noël 等人[Bull. London Math. Soc. 56, 2529 (2024)]引入的构造,证明了在几乎平坦的磁屏障域上涉及磁阶场的新有效算子的边界态存在。这一结果强调了这样一个事实,即即使不连续区域很小的不光滑度也会导致出现低于本征谱的特征值。我们还给出了出现这种有效算子的一个例子。
Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers
The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-Noël et al. [Bull. London Math. Soc. 56, 2529 (2024)] to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.