Time-averaged limit measure of the Wojcik model
Time-averaged limit measure of the Wojcik model
复制标题
Wojcik 模型的时间平均极限测量
DOI：
10.26421/qic15.1-2-7
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
N. Konno
中科院分区：
文献类型：
--
作者：
T. Endo;N. Konno
我们研究了Wojcik等人[1]提出并研究的“Wojcik模型”，它是一种在原点具有单一相位的单缺陷量子行走（QW）。他们报告说，在一个点上给出一个相位会对本地化产生惊人的影响。在量子阱的研究中，有三类测度起着重要的作用：时均极限测度、弱极限测度和平稳测度。前两种测量结果表明量子阱中局域行为和弹道扩散共存。正如Konno等人[2]所指出的，对于某些单缺陷量子阱，时间平均极限和稳态测度是密切相关的。在本文中，我们专注于Wojcik模型的两个措施之间的关系。我们以前的工作[3]已经得到了平稳测度。在这里，我们通过几种方法得到时间平均极限测度。我们的结果表明，平稳测度是时间平均极限测度的一个特例。
We investigate "the Wojcik model" introduced and studied by Wojcik et al. [1], which is a one-defect quantum walk (QW) having a single phase at the origin. They reported that giving a phase at one point causes an astonishing effect for localization. Three types of measures have important roles in the study of QWs: time-averaged limit measure, weak limit measure, and stationary measure. The first two measures imply a coexistence of localized behavior and the ballistic spreading in the QW. As Konno et al. [2] suggested, the time-averaged limit and stationary measures are closely related to each other for some QWs with one defect. In this paper, we focus on a relation between the two measures for the Wojcik model. The stationary measure was already obtained by our previous work [3]. Here, we get the time-averaged limit measure by several methods. Our results show that the stationary measure is a special case of the time-averaged limit measure.