{"title":"Dispersive and Strichartz Estimates for Schrödinger Equation with One Aharonov–Bohm Solenoid in a Uniform Magnetic Field","authors":"Haoran Wang, Fang Zhang, Junyong Zhang","doi":"10.1007/s00023-024-01500-8","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain dispersive and Strichartz estimates for solutions to the Schrödinger equation with one Aharonov–Bohm solenoid in the uniform magnetic field. The main step of the proof is the construction of the Schrödinger kernel, and the main obstacle is to obtain the explicit representation of the kernel, which requires a large set of careful calculations. To overcome this obstacle, we plan to construct the Schrödinger kernel by two different strategies. The first one is to use the Poisson summation formula as Fanelli et al. (Adv Math 400:108333, 2022), while the second one relies on the Schulman–Sunada formula in Št’ovíček (Ann Phys 376:254–282, 2017), which reveals the intrinsic connections of the heat kernels on manifolds with group actions.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 8","pages":"3029 - 3054"},"PeriodicalIF":1.3000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s00023-024-01500-8","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 obtain dispersive and Strichartz estimates for solutions to the Schrödinger equation with one Aharonov–Bohm solenoid in the uniform magnetic field. The main step of the proof is the construction of the Schrödinger kernel, and the main obstacle is to obtain the explicit representation of the kernel, which requires a large set of careful calculations. To overcome this obstacle, we plan to construct the Schrödinger kernel by two different strategies. The first one is to use the Poisson summation formula as Fanelli et al. (Adv Math 400:108333, 2022), while the second one relies on the Schulman–Sunada formula in Št’ovíček (Ann Phys 376:254–282, 2017), which reveals the intrinsic connections of the heat kernels on manifolds with group actions.
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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