Work

Ground States of Nonlinear Fermionic Systems: From Power-Law Interactions to Logarithmic Sobolev Inequality

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.14568

Authors: Chen, Bin, Guo, Yujin, Luo, Yong, Yan, Zhenya

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Central China Normal University, Zhongyuan University of Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G3930043704, G3933406863, G6424238467, G7342254039, G8224396934

OpenAlex ID: W7213319185

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