Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs  

作　　者：S. Salimi M.A. Jafarizadeh 

机构地区：[1]Department of Physics, University of Kurdistan, Kurdistan 51664, Iran [2]Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz 51664, Iran [3]Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Iran [4]Research Institute for Fundamental Sciences, Tabriz 51664, Iran

出　　处：《Communications in Theoretical Physics》2009年第6期1003-1009,共7页理论物理通讯（英文版）

摘　　要：In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.

关 键 词：continuous-time random walk classical random walk quantum random walk direct product of graphs Cayley graphs 

分 类 号：O157.5[理学—数学] O211.62[理学—基础数学]