Absence of singular continuous spectra and embedded eigenvalues for one-dimensional quantum walks with general long-range coins
Absence of singular continuous spectra and embedded eigenvalues for one-dimensional quantum walks with general long-range coins
复制标题
一般远程硬币的一维量子行走缺乏奇异连续光谱和嵌入特征值
DOI：
10.1142/s0129055x22500167
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发表时间：
2022
影响因子：
1.8
通讯作者：
Wada Kazuyuki
中科院分区：
文献类型：
--
作者：
Maeda Masaya;Suzuki Akito;Wada Kazuyuki
本文是第三作者工作的继续，研究了硬币算符具有特殊长程扰动的量子行走。本文考虑了硬币算子的一般长程扰动，证明了不存在奇异连续谱和嵌入特征值。证明依赖于规范变换和广义本征函数（Jost解决方案）的建设，这是在短程情况下研究。
This paper is a continuation of work by the third author, which studied quantum walks with special long-range perturbations of the coin operator. In this paper, we consider general long-range perturbations of the coin operator and prove the non-existence of a singular continuous spectrum and embedded eigenvalues. The proof relies on the gauge transformation and construction of generalized eigenfunctions (Jost solutions) which was studied in the short-range case.