论文标题
拓扑引起的光谱行为：量子图的示例
Topologically induced spectral behavior: the example of quantum graphs
论文作者
论文摘要
这篇评论论文总结了第八届国际数学家国际大会作者发表的演讲内容。使用Schrödinger算子在公制图上的示例，显示出配置空间的非平凡拓扑会导致各种光谱类型。特别是，这表明频谱可能是纯点类型或具有cantor结构。我们还解决了有关开放频谱差距数量的问题，并表明它可能是非零和有限的。最后，受到最近尝试建模异常效果的尝试的启发，我们分析了一个顶点耦合，该耦合表现出由顶点度平价决定的高能量行为。
This review paper summarizes the contents of the talk given by the author at the 8th International Congress of Chinese Mathematicians. Using examples of Schrödinger operators on metric graphs, it is shown that a nontrivial topology of the configuration space can give rise to a rich variety of spectral types. In particular, it is shown that the spectrum may be of a pure point type or to have a Cantor structure. We also address the question about the number of open spectral gaps and show that it could be nonzero and finite. Finally, inspired by a recent attempt to model the anomalous Hall effect we analyze a vertex coupling which exhibits high-energy behavior determined by the vertex degree parity.
