One-dimensional three-state quantum walks: Weak limits and localization

被引：2

作者：

Ko, Chul Ki ^{[1
]}

Segawa, Etsuo ^{[2
]}

Yoo, Hyun Jae ^{[3
]}

机构：

[1] Yonsei Univ, Univ Coll, 85 Songdogwahak Ro, Inchon 21983, South Korea

[2] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, 6-3-09 Aramaki Aza, Sendai, Miyagi 9808579, Japan

[3] Hankyong Natl Univ, Dept Appl Math, 327 Jungang Ro, Anseong 17579, Gyeonggi Do, South Korea

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2016年 / 19卷 / 04期

基金：

新加坡国家研究基金会; 日本学术振兴会;

关键词：

Three-state quantum walks; limit distribution; moments; localization;

D O I：

10.1142/S0219025716500259

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate one-dimensional three-state quantum walks. We find a formula for the moments of the weak limit distribution via a vacuum expectation of powers of a self-adjoint operator. We use this formula to fully characterize the localization of three-state quantum walks in one dimension. The localization is also characterized by investing the eigenvectors of the evolution operator for the quantum walk. As a byproduct we clarify the concepts of localization differently used in the literature. We also study the continuous part of the limit distribution. For typical examples we show that the continuous part is the same kind as that of two-state quantum walks. We provide with explicit expressions for the density of the weak limits of some three-state quantum walks.

引用

页数：20

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