标题： 具有置换对称散射概率的量子图顶点 显示英文标题

标题： Quantum graph vertices with permutation-symmetric scattering probabilities

摘要： 量子图顶点的边界条件通常用一个酉矩阵$U$来表示。 观察到如果$U$最多有两个特征值，那么顶点的散射矩阵$\mathcal{S}(k)$是单位矩阵和一个固定厄米特酉矩阵的线性组合，我们构建具有此性质的顶点耦合：对于所有动量$k$，从第$j$条边到第$\ell$条边的透射概率与$(j,\ell)$无关，且所有的反射概率都相等。 我们根据它们的散射特性对这些耦合进行分类，这导致了广义的$\delta$和$\delta'$耦合的概念。 显示英文摘要

摘要： Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the identity matrix and a fixed Hermitian unitary matrix, we construct vertex couplings with this property: For all momenta $k$, the transmission probability from the $j$-th edge to $\ell$-th edge is independent of $(j,\ell)$, and all the reflection probabilities are equal. We classify these couplings according to their scattering properties, which leads to the concept of generalized $\delta$ and $\delta'$ couplings.