笛卡尔积量子图 Fermi 面可约的充分条件

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 907-918.

笛卡尔积量子图 Fermi 面可约的充分条件

韩雨婷¹(), 赵佳¹^,^*(), 张亚林²()

¹ 河北工业大学理学院天津 300401
² 天津理工大学理学院天津 300384

收稿日期:2025-02-19 修回日期:2025-06-27 出版日期:2026-06-26 发布日期:2026-06-17
通讯作者: 赵佳 E-mail:hyt481669@163.com;zhaojia@hebut.edu.cn;yalinzhang@tjut.edu.cn
作者简介:韩雨婷,E-mail:hyt481669@163.com;
张亚林,E-mail:yalinzhang@tjut.edu.cn
基金资助:
国家自然科学基金(12201460);河北省自然科学基金面上项目(A2024202017)

Sufficient Conditions for Reducibility of Fermi Surfaces in Cartesian Product Quantum Graphs

Yuting Han¹(), Jia Zhao¹^,^*(), Yalin Zhang²()

¹ School of Science, Hebei University of Technology, Tianjin 300401
² Department of Mathematics, Tianjin University of Technology, Tianjin 300384

Received:2025-02-19 Revised:2025-06-27 Online:2026-06-26 Published:2026-06-17
Contact: Jia Zhao E-mail:hyt481669@163.com;zhaojia@hebut.edu.cn;yalinzhang@tjut.edu.cn
Supported by:
NSFC(12201460);Hebei NSF(A2024202017)

摘要/Abstract

摘要：

为了研究周期量子图在 Fermi 面可约条件下嵌入特征值的存在性和相关特征函数的性质, 该文构造了两类周期笛卡尔积量子图, 证明了在单层周期量子图基本域只有两个顶点且满足一定条件时, 两类笛卡尔积量子图的 Fermi 面都是可约的, 并对基本域的选取条件进行了补充.

关键词: 量子图, 度量图, 微分算子, 周期 Schr?dinger 算子, 可约 Fermi 面.

Abstract:

In order to investigate the existence of embedded eigenvalues and the properties of related characteristic functions of periodic quantum graphs under the condition of Fermi surface reducibility, this paper constructs two types of periodic Cartesian product quantum graphs. It is proved that when the foundation domain of a single-layer periodic quantum graph has only two vertices and certain conditions are met, the Fermi surfaces of both types of Cartesian product quantum graphs are reducible, and the selection conditions of the foundation domain are supplemented.}

Key words: quantum graphs, metric graphs, differential operators, periodic Schr?dinger operators, reducible Fermi surface.

中图分类号:

O175.3

韩雨婷, 赵佳, 张亚林. 笛卡尔积量子图 Fermi 面可约的充分条件[J]. 数学物理学报, 2026, 46(3): 907-918.

Yuting Han, Jia Zhao, Yalin Zhang. Sufficient Conditions for Reducibility of Fermi Surfaces in Cartesian Product Quantum Graphs[J]. Acta mathematica scientia,Series A, 2026, 46(3): 907-918.

图/表 4

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