{"title":"具有库仑势的费米子非线性薛定谔系统的基态 I：\\(L^2\\)-次临界情况","authors":"Bin Chen, Yujin Guo","doi":"10.1007/s11005-024-01877-x","DOIUrl":null,"url":null,"abstract":"<div><p>We consider ground states of the <i>N</i> coupled fermionic nonlinear Schrödinger systems with the Coulomb potential <i>V</i>(<i>x</i>) in the <span>\\(L^2\\)</span>-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter <span>\\(\\alpha >0\\)</span>, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as <span>\\(\\alpha \\rightarrow \\infty \\)</span>, where the mass concentrates at one of the singular points for the Coulomb potential <i>V</i>(<i>x</i>).\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the \\\\(L^2\\\\)-subcritical case\",\"authors\":\"Bin Chen, Yujin Guo\",\"doi\":\"10.1007/s11005-024-01877-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider ground states of the <i>N</i> coupled fermionic nonlinear Schrödinger systems with the Coulomb potential <i>V</i>(<i>x</i>) in the <span>\\\\(L^2\\\\)</span>-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter <span>\\\\(\\\\alpha >0\\\\)</span>, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as <span>\\\\(\\\\alpha \\\\rightarrow \\\\infty \\\\)</span>, where the mass concentrates at one of the singular points for the Coulomb potential <i>V</i>(<i>x</i>).\\n</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"114 6\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01877-x\",\"RegionNum\":3,\"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":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01877-x","RegionNum":3,"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}
Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the \(L^2\)-subcritical case
We consider ground states of the N coupled fermionic nonlinear Schrödinger systems with the Coulomb potential V(x) in the \(L^2\)-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter \(\alpha >0\), which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as \(\alpha \rightarrow \infty \), where the mass concentrates at one of the singular points for the Coulomb potential V(x).
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The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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