{"title":"Existence and Linear Stability of Symmetric Periodic Orbits in the Generalized Planar Stark–Zeeman Problem","authors":"Angelo Alberti","doi":"10.1007/s12346-024-01087-9","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this paper is to demonstrate the existence of symmetric periodic solutions for a two-dimensional hydrogen atom subject to external electric and magnetic fields. We build upon the analysis of periodic orbits that was initially performed by De Bustos et al. (J Math Phys 53:082701, 2012). In this study, we utilize the symmetry of reflection and an appropriate set of variables to obtain results regarding the existence and stability of periodic solutions. Furthermore, we determine the presence of KAM 2-tori that enclose some of the linearly stable periodic solutions.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01087-9","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The purpose of this paper is to demonstrate the existence of symmetric periodic solutions for a two-dimensional hydrogen atom subject to external electric and magnetic fields. We build upon the analysis of periodic orbits that was initially performed by De Bustos et al. (J Math Phys 53:082701, 2012). In this study, we utilize the symmetry of reflection and an appropriate set of variables to obtain results regarding the existence and stability of periodic solutions. Furthermore, we determine the presence of KAM 2-tori that enclose some of the linearly stable periodic solutions.
本文旨在证明受外部电场和磁场作用的二维氢原子存在对称周期解。我们以 De Bustos 等人最初进行的周期轨道分析为基础（J Math Phys 53:082701, 2012）。在这项研究中，我们利用反射对称性和一组适当的变量，获得了有关周期性解的存在性和稳定性的结果。此外，我们还确定了包围某些线性稳定周期解的 KAM 2-Tori 的存在。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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