Strongly trapped space-inhomogeneous quantum walks in one dimension
Strongly trapped space-inhomogeneous quantum walks in one dimension
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DOI：
10.1007/s11128-022-03674-8
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发表时间：
2021-05
影响因子：
2.5
通讯作者：
Chusei Kiumi;Kei Saito
中科院分区：
文献类型：
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作者：
Chusei Kiumi;Kei Saito
定域化是一维整数格点上离散时间空间非均匀量子行走的一个特征现象，其中粒子围绕其初始位置保持定域化。时间演化算子特征值的存在是局部化发生的充分必要条件，其相关特征向量与局部化量有着深刻的关系，即，步行者在长时间限制内停留在起始位置附近的概率。在作者先前的研究中，使用转移矩阵研究了具有一个缺陷的两相量子行走的本征值，该转移矩阵专注于局域化的发生（Kiumi和Saito in Quantum Inf Process 20（5）：1-11，2021）。在本文中，我们介绍了使用传输矩阵计算本征向量的解析方法，并将我们的结果进行了推广和简化，不仅可以表征具有一个缺陷的两相量子行走的本征值，而且可以表征具有有限个缺陷的更一般的空间非均匀模型的本征值。利用这些结果，我们定量地评估本地化和研究强捕获性能，通过推导的时间平均极限分布的五个模型研究以前。
Localization is a characteristic phenomenon of discrete-time space-inhomogeneous quantum walks on the one-dimensional integer lattice, where particles remain localized around their initial position. The existence of eigenvalues of time evolution operators is a necessary and sufficient condition for the occurrence of localization, and their associated eigenvectors are deeply related to the amount of localization, i.e., the probability that the walker stays around the starting position in the long-time limit. In a previous study by authors, the eigenvalues of two-phase quantum walks with one defect were studied using a transfer matrix, which focused on the occurrence of localization (Kiumi and Saito in Quantum Inf Process 20(5): 1-11, 2021). In this paper, we introduce the analytical method to calculate eigenvectors using the transfer matrix and also extend and simplify our results to characterize eigenvalues not only for two-phase quantum walks with one defect but also for a more general space-inhomogeneous model with a finite number of defects. With these results, we quantitatively evaluate localization and study the strong trapping property by deriving the time-averaged limit distributions of five models studied previously.