周期图的平坦带

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-04-13 DOI:10.1063/5.0156336

Mostafa Sabri, Pierre Youssef

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引用次数: 5

摘要

我们研究了欧几里德空间中周期图的平坦带。这些是相应邻接矩阵的无限退化特征值，具有紧支持的特征向量。我们提供了一些生成所需波段的最佳配方和图形具有平坦波段的充分条件，我们描述了特征向量占用单个单元的平坦波段集合，并计算了小单元的这些波段列表。接下来我们讨论在特殊情况下平带的稳定性和稀有性。更多的民间传说结果得到了证实，许多问题仍未解决。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Flat bands of periodic graphs

We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support. We provide some optimal recipes to generate desired bands and some sufficient conditions for a graph to have flat bands, we characterize the set of flat bands whose eigenvectors occupy a single cell, and we compute the list of such bands for small cells. We next discuss the stability and rarity of flat bands in special cases. Additional folklore results are proved, and many questions are still open.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.