论文标题
首选方向的磁环链与顶点耦合
Magnetic ring chains with vertex coupling of a preferred orientation
论文作者
论文摘要
我们讨论了一个周期性量子图的光谱特性，该量子图由连接链接紧密或松散耦合的环组成，假设顶点耦合显然在时间反向和均匀的磁场垂直于图平面的均相磁场方面显然是不变的。结果表明，顶点奇偶校验决定了高能量下的光谱行为，并且每当边缘不稳定时，带 - berkolaiko通用性就会保持。磁场会影响一个能量属于紧密链情况下光谱的可能性，并且还可以将一些光谱带变成无限退化的特征值。
We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time reversal and a homogeneous magnetic field perpendicular to the graph plane is present. It is shown that the vertex parity determines the spectral behavior at high energies and the Band-Berkolaiko universality holds whenever the edges are incommensurate. The magnetic field influences the probability that an energy belongs to the spectrum in the tight-chain case, and also it can turn some spectral bands into infinitely degenerate eigenvalues.
