Abstract

We discuss quantum graphs with the vertex coupling which violates the time-reversal invariance. For a simple type of this coupling in which the violation is in a sense maximum one we show that it leads to spectral properties determined in the high-energy regime by the graph topology. We illustrate this effect on examples which involve lattice graphs and loop arrays as well as finite graphs associated with Platonic solids. We also show that transport properties of such graphs may differ in the graph bulk and at the edges.

中文翻译：

---

顶点违反时间反转对称性的量子图

摘要

我们讨论了具有顶点耦合的量子图，它违反了时间反转不变性。对于这种类型的简单耦合，其中违反在某种意义上是最大的，我们表明它导致了由图拓扑在高能态中确定的光谱特性。我们在涉及晶格图和回路阵列以及与柏拉图固体相关的有限图的示例中说明了这种影响。我们还表明，此类图的传输特性可能在图的体积和边缘处有所不同。