三周期量子行走的布洛赫振荡及拓扑特性  

The Bloch Oscillation and Topological Properties of Three-period Quantum Walk

作　　者：李小萍 李志坚[1] LI Xiaoping;LI Zhijian(Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学理论物理研究所,山西太原030006

出　　处：《山西大学学报（自然科学版）》2024年第4期786-791,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12147215)。

摘　　要：本文推广一维无限长格点线上三周期量子行走模型,引入两个非对称相位累积算符,计算系统的能带结构和表征系统拓扑特性的绕数,用量子行走过程中累积的相位表示出绕数。进一步引入含时相位,研究三周期量子行走的动力学,发现其概率分布表现出类似一维晶格中电子在电场作用下的布洛赫振荡行为。特别地,三周期量子行走的拓扑绕数与布洛赫振荡一个周期内的转折点数相等,从系统动力学演化的角度表征了系统的拓扑特性。In this work,the three-period quantum walk model on one-dimensional infinite lattice line is extended to include two asymmetric phase-accumulating operators.The energy band structure and the winding number,which characters the topological properties of the system,are calculated.The winding number is represented by the phase accumulation in the process of quantum walk.Furthermore,we introduce the time-dependent phase and investigate the dynamics of three-period quantum walk.It is found that the probability distribution behaves Bloch oscillation as that an electron subjected to a constant electric field in a one-dimensional lattice.In particular,the topological winding number of three-period quantum walk is equal to the number of turning points over a period of Bloch oscillation.As a conclusion,the topological properties of the system can be viewed from the point of system dynamical evolution.

关 键 词：量子行走 布洛赫振荡 拓扑特性 

分 类 号：O436[机械工程—光学工程]