Study on stochastic and quantum models on complex networks

关于一维两态空间的齐次量子游动，已有许多结果。因此，我们研究了一些扩展模型的局部化和极限定理。实际上，我们考虑的是带有一个缺陷的一维量子行走。在此模型中，我们得到了局部化的充要条件和弱极限定理。进而得到了阈值模型的特征值和特征向量。利用它们分析了该模型上连续时间量子游走的极限测度，阐明了量子游走与相应的经典随机游走的区别。

There are many results on two-state space homogeneous quantum walks in one dimension. Therefore we investigated localization and limit theorems for some extended models. In fact we considered the one-dimensional quantum walk with one defect. In this model, we obtained necessary and sufficient conditions of localization and the weak limit theorems. Furthermore we got the eigenvalue and eigenvector of the threshold model. By using them, we analyzed limit measures of the continuous-time quantum walk on the model and clarified difference between the quantum walk and the corresponding classical random walk.