- 著者
- Takako ENDO Hikari KAWAI Norio KONNO
- 出版者
- 東北大学大学院情報科学研究科ジャーナル編集委員会
- 雑誌
- Interdisciplinary Information Sciences (ISSN:13409050)
- 巻号頁・発行日
- vol.23, no.1, pp.57-64, 2017 (Released:2017-03-31)
- 参考文献数
- 22
- 被引用文献数
- 2
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 matrices except at one defected point. In this paper, we call the QW defined by diagonal unitary matrices, ``the diagonal QW'', and we consider the stationary distributions of general 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 are stationary measures 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.
- 著者
- Shimpei ENDO Takako ENDO Norio KONNO Etsuo SEGAWA Masato TAKEI
- 出版者
- 東北大学大学院情報科学研究科ジャーナル編集委員会
- 雑誌
- Interdisciplinary Information Sciences (ISSN:13409050)
- 巻号頁・発行日
- pp.2016.R.01, (Released:2016-03-25)
- 参考文献数
- 24
- 被引用文献数
- 6
We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW ``the two-phase QW with one defect'', which we treated concerning localization theorems. The two-phase QW with one defect has been expected to be a mathematical model of topological insulator which is an intense issue both theoretically and experimentally. In this paper, we derive the weak limit theorem describing the ballistic spreading, and as a result, we obtain the mathematical expression of the whole picture of the asymptotic behavior. Our approach is based mainly on the generating function of the weight of the passages. We emphasize that the time-averaged limit measure is symmetric for the origin , however, the weak limit measure is asymmetric, which implies that the weak limit theorem represents the asymmetry of the probability distribution.