发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Central China Normal University; School of Mathematics and Information Science, Zhongyuan University of Technology; State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 华中师范大学; 中原工学院数学与信息科学学院; 中国科学院数学与系统科学研究院数学科学国家重点实验室; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究双分量对数费米子系统的基态，证明其是幂律系统在p趋近1时的L^∞极限，并建立正交函数的锐利对数Sobolev不等式。
AI 中文摘要
我们考虑在$\mathbb{R}^d$（其中$d\ge 1$为任意维数）中的双分量对数费米子系统的基态。我们证明，在平移和缩放的意义下，对数系统的基态是当$p\searrow 1$时双分量$2p-1$幂律费米子系统基态的$L^\infty$极限。作为副产品，我们还建立了$\mathbb{R}^d$中正交函数的一个锐利对数Sobolev不等式，其优化元在缩放意义下是对数系统相关的约束变分问题的极小元。
英文摘要
We consider ground states of a two-component logarithmic fermionic system in $\mathbb{R}^d$, where $d\ge 1$ is arbitrary. We prove that up to translations and scalings, ground states of the logarithmic system are the $L^\infty $-limits of ground states for a two-component $2p-1$ power-law fermionic system as $p\searrow 1$. As a byproduct, we also establish a sharp logarithmic Sobolev inequality for orthonormal functions in \(\mathbb{R}^d\), whose optimizers are, up to scalings, the minimizers of a constraint variational problem associated with the logarithmic system.
