论文标题
具有时间反转的非不变顶点耦合的周期链图频谱
Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling
论文作者
论文摘要
我们以周期性环的形式研究了量子图的光谱特性，并在每个相邻对之间具有连接的链接，假设在顶点处的波函数是通过时间反转的明显不变的条件匹配的。我们尤其讨论了此类系统的高能行为和限制情况时，当这种图的基本细胞中的一个边缘缩小到零时。频谱取决于图的拓扑和几何形状。能量属于频谱的概率采用三种反映出顶点奇偶和镜像对称性的值，并且带模式受图形边缘长度的可比性的影响。
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly non-invariant with respect to time reversal. We discuss, in particular, the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero. The spectrum depends on the topology and geometry of the graph. The probability that an energy belongs to the spectrum takes three different values reflecting the vertex parities and mirror symmetry, and the band patterns are influenced by commensurability of graph edge lengths.
