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arXiv · 2312.06916

Ground States of Fermionic Nonlinear Schr\"{o}dinger Systems with Coulomb Potential II: The $L^2$-Critical Case

Bin Chen·Yujin Guo·Shu Zhang
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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 $0<a<a^*_N$, where the critical constant $0<a^*_N<\infty$ is the same as the best constant of a dual finite-rank Lieb-Thirring inequality. By developing the so-called blow-up analysis of many-body fermionic problems, we also prove the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$.

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Bin Chen, Yujin Guo, Shu Zhang. 2023-12-12. Ground States of Fermionic Nonlinear Schr\"{o}dinger Systems with Coulomb Potential II: The $L^2$-Critical Case. https://arxiv.org/abs/2312.06916

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