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

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-11-14 DOI:10.1007/s11005-024-01877-x

Bin Chen, Yujin Guo

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引用次数: 0

摘要

我们考虑了在\(L^2\)-次临界情况下具有库仑势V(x)的N个耦合费米子非线性薛定谔系统的基态。通过研究相关的约束变分问题，我们证明了任意参数（\α >0\）下系统基态的存在，该参数代表了非相对论量子粒子的吸引力强度。我们还分析了该系统基态的极限行为（\(\alpha \rightarrow \infty \），其中质量集中在库仑势 V(x) 的奇异点之一。

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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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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

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.