论文标题
量子步行在现实世界中复杂网络上的无元素值定位
Null-eigenvalue localization of quantum walks on real-world complex networks
论文作者
论文摘要
首先，我们报告现实世界中复杂网络的邻接矩阵系统地具有比随机网络更高的尺寸为空特征。这些无效的特征值是由复制机制引起的，导致具有局部对称性的结构，这些结构应该在复杂的组织中更存在。这些状态的相关特征向量是强烈的定位。然后，我们在量子力学的背景下评估这些微观结构，通过研究连续时间量子步行的传播来证明前面提到的定位。在以下几点中，这种无效的本地化本质与安德森本地化基本不同：首先，特征值不在国家密度的边缘，而是位于其中心。其次，本征态不会呈指数衰减，也不会从对称结构中泄漏出来。从这个意义上讲，它更接近连续体中的约束状态。
First we report that the adjacency matrices of real-world complex networks systematically have null eigenspaces with much higher dimensions than that of random networks. These null eigenvalues are caused by duplication mechanisms leading to structures with local symmetries which should be more present in complex organizations. The associated eigenvectors of these states are strongly localized. We then evaluate these microstructures in the context of quantum mechanics, demonstrating the previously mentioned localization by studying the spread of continuous-time quantum walks. This null-eigenvalue localization is essentially different from the Anderson localization in the following points: first, the eigenvalues do not lie on the edges of the density of states but at its center; second, the eigenstates do not decay exponentially and do not leak out of the symmetric structures. In this sense, it is closer to the bound state in continuum.
