An eigenfunction expansion formula for one-dimensional two-state quantum walks
An eigenfunction expansion formula for one-dimensional two-state quantum walks
复制标题
一维二维量子行走的本征函数展开式
DOI：
10.1007/s43034-022-00210-8
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发表时间：
2022
影响因子：
1
通讯作者：
Tate Tatsuya
中科院分区：
文献类型：
--
作者：
Yuji Sano;Hiroshi Sato and Yusuke Suyama;石田弘隆;Tate Tatsuya
本文的目的是给出一维两态量子行走的本征函数展开公式的一个直接证明，该公式与Weyl，Stone，Titchmarsh和科代拉关于Sturm-Liouville算符的本征函数展开公式类似.在CMV矩阵理论的背景下，它已经由Gesztesy-Zinchenko建立。我们的方法仅限于上面提到的量子行走类，而它是直接的，它给出了绿色函数的一些重要性质。这里给出的性质使我们能够给出正矩阵值测度的具体公式，在所谓两相模型的最简单情况下，它直接给出谱测度。
The purpose of this paper is to give a direct proof of an eigenfunction expansion formula for one-dimensional two-state quantum walks, which is an analog of that for Sturm–Liouville operators due to Weyl, Stone, Titchmarsh, and Kodaira. In the context of the theory of CMV matrices, it had been already established by Gesztesy–Zinchenko. Our approach is restricted to the class of quantum walks mentioned above, whereas it is direct and it gives some important properties of Green functions. The properties given here enable us to give a concrete formula for a positive-matrix-valued measure, which gives directly the spectral measure, in a simplest case of the so-called two-phase model.
( 18 ) 二阶常微分方程的特征值问题和海森堡S矩阵理论
影响因子：
1.7
作者：
K. Kodaira
通讯作者：
K. Kodaira