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一维环上量子随机行走演化算符的本征值和本征态

发表时间:2016-04-15  浏览量:1944  下载量:713
全部作者: 李应天,徐新平
作者单位: 苏州大学物理科学与技术学院
摘 要: 利用切比雪夫多项式(Chebyshev polynomial)方法,首次推导了一维环上离散时间量子随机行走演化算符的本征值和本征态。计算结果表明,演化算符的本征值与第一类切比雪夫多项式有关,其本征态与凝聚态物理中的布里赫(Bloch)函数有关。计算结果为定量分析离散时间量子随机行走的动力学性质奠定了重要基础。
关 键 词: 理论物理学;统计物理与复杂系统;随机行走;量子随机行走;复杂网络
Title: Eigenvalues and eigenstates of the evolution operator of quantum walks on cycles
Author: LI Yingtian, XU Xinping
Organization: School of Physical Science and Technology, Soochow University
Abstract: We investigate the eigenvalues and eigenstates of the evolution operator of the discrete-time quantum random walk on the cycles. Using the Chebyshev polynomial method, we derive exact analytical expression of the eigenvalues and eigenstates of the evolution operator for the first time. It is found that the eigenvalues of the evolution operator are closely related to the Chebyshev polynomial of the first kind, the eigenstates of the evolution operator are closely related to the Bloch function in condensed matter physics. Our results provide important information to analyze the dynamical properties of discrete-time quantum random walk.
Key words: theoretical physics; statistical physics and complex system; random walk; quantum random walk; complex network
发表期数: 2016年4月第7期
引用格式: 李应天,徐新平. 一维环上量子随机行走演化算符的本征值和本征态[J]. 中国科技论文在线精品论文,2016,9(7):683-687.
 
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