笛卡尔积量子图 Fermi 面可约的充分条件

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (3): 907-918.

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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)

Abstract

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.

CLC Number:

O175.3

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.

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References 11

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

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