{"title":"Schrödinger Operators with Multiple Aharonov–Bohm Fluxes","authors":"Michele Correggi, Davide Fermi","doi":"10.1007/s00023-024-01446-x","DOIUrl":null,"url":null,"abstract":"<p>We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of <span>\\( N \\geqslant 1\\)</span> Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.\n</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"60 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-05-25","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/s00023-024-01446-x","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
Abstract
We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of \( N \geqslant 1\) Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.
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.
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