7、图顶点条件相关研究

图顶点条件相关研究

1. 二度顶点的标准条件与散射矩阵

对于二度顶点，标准顶点条件可写为如下形式：
[
i
\begin{pmatrix}
-2 + \frac{2}{d} & \frac{2}{d} & \frac{2}{d} & \cdots \
\frac{2}{d} & -2 + \frac{2}{d} & \frac{2}{d} & \cdots \
\frac{2}{d} & \frac{2}{d} & -2 + \frac{2}{d} & \cdots \
\vdots & \vdots & \vdots & \ddots
\end{pmatrix}
\vec{u}
=
\begin{pmatrix}
\frac{2}{d} & \frac{2}{d} & \frac{2}{d} & \cdots \
\frac{2}{d} & \frac{2}{d} & \frac{2}{d} & \cdots \
\frac{2}{d} & \frac{2}{d} & \frac{2}{d} & \cdots \
\vdots & \vdots & \vdots & \ddots
\end{pmatrix}
\partial\vec{u}
]
其散射矩阵与能量无关，可通过两个投影算子表示。引入对应特征值(\pm1)的特征子空间(N_1 = L