量子链中的反常束缚态
Unusual Bound States in Quantum Chains
摘要：
在量子力学中，束缚态的存在性一直是人们感兴趣的课题。连接到无限引线的交叉线和空腔是典型的例子，其中具有凸起的开放几何形状支持二维或多维的约束解。在这里，我们发现，拓扑结构的作用甚至可以比空间的可用性更重要，通过显示在一维系统，如量子交叉链，并在一般情况下，链绑定在几何没有循环的约束解的存在。它表明，这些不寻常的结合的例子可以解决的能量和本征向量分析。由于所讨论的效应具有波状性质，因此以紧束缚电磁谐振器阵列的形式给出了一个实验提案。
英文摘要：
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges support bound solutions, in two or more dimensions. Here we find that the role of topology can be even more important than space availability, by showing the existence of bound solutions in one-dimensional systems such as quantum cross-chains and, in general, chains tied in geometries without loops. It is shown that these examples of unusual binding can be solved analitically for energies and eigenvectors. An experimental proposal is given in the form of tight-binding arrays of electromagnetic resonators, as the effects in question are of a wave-like nature.
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