Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential II: The $L^2$-Critical Case

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-12 DOI:arxiv-2312.06916

Bin Chen, Yujin Guo, Shu Zhang

引用次数: 0

Abstract

As a continuation of \cite{me}, we consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger system with a parameter $a $ and the Coulomb potential $V(x)$ in the $L^2$-critical case, where $a>0$ represents the attractive strength of the quantum particles. For any given $N\in\mathbb{N}^+$, we prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0

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具有库仑势的费米子非线性薛定谔系统的基态 II：L^2 美元临界情形

作为\cite{me}的延续，我们考虑了具有参数$a $和库仑势$V(x)$的$N$耦合微分非线性Schrödinger系统在$L^2$临界情况下的基态，其中$a>0$表示量子粒子的吸引强度。对于任意给定的$N\in\mathbb{N}^+$，我们证明了系统存在基态，当且仅当吸引强度$a$满足$0

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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