论文标题
通过散射来区分共云的量子图
Distinguishing co-spectral quantum graphs by scattering
论文作者
论文摘要
我们提出了一种简单的方法，用于解决公制图上Schrödinger操作员共同光谱的方法。我们的方法包括将引线附加到它们上，并比较这些（非压缩）图上相应散射问题的$ s $功能。 我们表明，在某些情况下，包括最多6个顶点的一般图，最多9个顶点的一般树以及一般的模糊球 - 特征值和散射数据足以区分共光谱度量图。
We propose a simple method for resolution of co-spectrality of Schrödinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the $S$-functions of the corresponding scattering problems on these (non-compact) graphs. We show that in several cases -- including general graphs on at most 6 vertices, general trees on at most 9 vertices, and general fuzzy balls -- eigenvalues and scattering data are together sufficient to distinguish co-spectral metric graphs.
