Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials

Fuente: arXiv
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Autores principales: Guo, Yujin, Li, Yan, Wu, Shuang
Formato: Preprint
Publicado: 2026
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author Guo, Yujin
Li, Yan
Wu, Shuang
author_facet Guo, Yujin
Li, Yan
Wu, Shuang
contents As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schrödinger systems with attractive interactions in $\mathbb{R}^3$, which are trapped in ring-shaped potentials. For any given $N\in\mathbb{N}^+$, we prove that ground states exist if $0<a<a_N^*$, where $a$ denotes the strength of attractive interactions in the system, and $a_N^*$ is the best constant of a finite-rank Lieb-Thirring inequality. Moreover, for some $N\in\mathbb{N}^+$, we also prove the nonexistence of minimizers for the system as soon as $a\geq a_N^*$. Applying the energy estimates and the blow-up analysis, we further analyze the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$.
format Preprint
id arxiv_https___arxiv_org_abs_2603_05903
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials
Guo, Yujin
Li, Yan
Wu, Shuang
Analysis of PDEs
As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schrödinger systems with attractive interactions in $\mathbb{R}^3$, which are trapped in ring-shaped potentials. For any given $N\in\mathbb{N}^+$, we prove that ground states exist if $0<a<a_N^*$, where $a$ denotes the strength of attractive interactions in the system, and $a_N^*$ is the best constant of a finite-rank Lieb-Thirring inequality. Moreover, for some $N\in\mathbb{N}^+$, we also prove the nonexistence of minimizers for the system as soon as $a\geq a_N^*$. Applying the energy estimates and the blow-up analysis, we further analyze the mass concentration behavior of ground states for the system as $a\nearrow a_N^*$.
title Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials
topic Analysis of PDEs
url https://arxiv.org/abs/2603.05903