{"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}
引用次数: 0
Abstract
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).
期刊介绍：
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
