标题： 对角量子行走中有一个缺陷的平稳测度 显示英文标题

标题： The stationary measure for diagonal quantum walk with one defect

摘要： 本研究受到先前工作[14]的启发。 我们处理三种一维量子行走（QWs），其时间演化由对角线酉矩阵和带有缺陷的一个对角线酉矩阵描述。 在本文中，我们将由对角线酉矩阵定义的QW称为“对角线QW”，并考虑一般二态带有一个缺陷的对角线QW、三态空间均匀的对角线QW以及三态带有一个缺陷的对角线QW的平稳分布。 我们研究的一个目的是通过平稳测度来表征QWs，这可能会导致回答基本而自然的问题，“一维QWs的平稳测度是什么？” 为了分析平稳分布，我们关注相应的特征值问题和平稳测度的定义。 显示英文摘要

摘要： This study is motivated by the previous work [14]. We treat 3 types of the one-dimensional quantum walks (QWs), whose time evolutions are described by diagonal unitary matrix, and diagonal unitary matrices with one defect. In this paper, we call the QW defined by diagonal unitary matrices, "the diagonal QW", and we consider the stationary distributions of generally 2-state diagonal QW with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW with one defect. One of the purposes of our study is to characterize the QWs by the stationary measure, which may lead to answer the basic and natural question, "What the stationary measure is for one-dimensional QWs ?". In order to analyze the stationary distribution, we focus on the corresponding eigenvalue problems and the definition of the stationary measure.