论文标题
常规量子树的光谱：流氓特征值和对顶点条件的依赖
Spectra of Regular Quantum Trees: Rogue Eigenvalues and Dependence on Vertex Condition
论文作者
论文摘要
我们通过与正交多项式的关系，在有限的常规公制树上研究Schrödinger运算符的频谱，该公制提供了图形透视。由于Robin顶点参数趋向于$ - \ infty $，因此有限的许多特征值趋向于$ - \ infty $，而群集上方的特征值则从下方保持界限。某些“流氓”特征值脱离了这个集群，往往更快地倾向于$ - \ infty $。可以将光谱视为平面中两个对象的相交点 - 螺旋曲线取决于schrödinger电位，以及一组曲线，具体取决于分支因子，树的直径和罗宾参数。
We investigate the spectrum of Schrödinger operators on finite regular metric trees through a relation to orthogonal polynomials that provides a graphical perspective. As the Robin vertex parameter tends to $-\infty$, a narrow cluster of finitely many eigenvalues tends to $-\infty$, while the eigenvalues above the cluster remain bounded from below. Certain "rogue" eigenvalues break away from this cluster and tend even faster toward $-\infty$. The spectrum can be visualized as the intersection points of two objects in the plane--a spiral curve depending on the Schrödinger potential, and a set of curves depending on the branching factor, the diameter of the tree, and the Robin parameter.
