Eigenvalues and threshold resonances of a two-dimensional split-step quantum walk with strong shift

被引：1

作者：

Fuda, Toru ^{[1
]}

Funakawa, Daiju ^{[2
]}

Sasayama, Satoshi ^{[3
]}

Suzuki, Akito ^{[4
]}

机构：

[1] Kokushikan Univ, Sch Sci & Engn, Setagaya, Tokyo 1548515, Japan

[2] Hokkai Gakuen Univ, Dept Elect & Informat Engn, Sapporo 0628605, Japan

[3] Hokkaido Informat Univ, Dept Informat Media, Nishi-Nopporo 59-2, Ebetsu, Hokkaido 0698585, Japan

[4] Shinshu Univ, Fac Engn, Div Math & Phys, Wakasato, Nagano 3808553, Japan

来源：

QUANTUM STUDIES-MATHEMATICS AND FOUNDATIONS | 2023年 / 10卷 / 04期

关键词：

Quantum walks; Spectral analysis; Localization; Resonances;

D O I：

10.1007/s40509-023-00307-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we derive sufficient conditions for the localization of two-dimensional split-step quantum walks with a strong shift. For this purpose, we analyze the zero points of the function f introduced by Fuda et al. (Quantum Inf Process 16(8), 203, 2017) and make these zero points explicit. These zeros provide a concrete representation of the eigenvalues and eigenvectors of the evolution operator, and in particular, clarify where localization occurs. In addition, the eigenvalues obtained here asymptotically approach threshold resonance in special cases. We also describe the display of threshold resonances and generalized eigenfunctions.

引用

页码：483 / 496

页数：14

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