Null-eigenvalue localization of quantum walks on complex networks
Null-eigenvalue localization of quantum walks on complex networks
复制标题
复杂网络上量子行走的零特征值局域化
DOI：
10.1103/physrevresearch.2.033185
复制
发表时间：
2020
影响因子：
4.2
通讯作者：
Hatano Naomichi
中科院分区：
文献类型：
--
作者：
Bueno Ruben;Hatano Naomichi
首先，我们报告说，现实世界的复杂网络的邻接矩阵系统地具有零特征空间的维数比随机网络高得多。这些零特征值是由复制机制导致的，这种机制导致了具有局部对称性的结构，这种结构在复杂的组织中应该更常见。这些态的相关本征向量是强局域化的。然后，我们在量子力学的背景下评估这些微结构，通过研究连续时间量子行走的传播来证明前面提到的局部化。这种零本征值局域化与安德森局域化的本质区别在于：首先，本征值不位于态密度的边缘，而是位于态密度的中心;其次，本征态不按指数衰减，也不从对称结构中泄漏。在这个意义上，它更接近连续统中的束缚态。
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.