论文标题
没有奇异的连续光谱和嵌入的特征值一维量子步行
Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins
论文作者
论文摘要
本文是第三作者的纸\ cite {w}的延续，该论文研究了量子步行，并使用了硬币操作员的特殊远程扰动。在本文中，我们考虑了硬币操作员的一般远程扰动，并证明了单数连续频谱和嵌入特征值的不存在。证明依赖于在\ cite {MSSSSDIS}中的短程案例中研究的广义本征函数（JOST解决方案）的构建。
This paper is a continuation of the paper \cite{W} 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 construction of generalized eigenfunctions (Jost solutions) which was studied in the short-range case in \cite{MSSSSdis}.
