一维准周期马赛克晶格中量子扩散性质研究  

Quantum diffusion in the one-dimensional quasi-periodic mosaic lattice

作　　者：万敏慧 李函泽 钟建新 WAN Minhui;LI Hanze;ZHONG Jianxin(Department of Physics and Optoelectronics,Xiangtan University,Xiangtan 411105,China;Institute for Quantum Science and Technology,Shanghai University,Shanghai 200444,China)

机构地区：[1]湘潭大学物理与光电工程学院,湖南湘潭411105 [2]上海大学量子科技研究院,上海200444

出　　处：《湘潭大学学报（自然科学版）》2024年第5期12-20,共9页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(12374046)。

摘　　要：基于紧束缚哈密顿量,对一维准周期Aubry-André-Harper(AAH)马赛克晶格模型中量子扩散性质进行探究.通过计算模型的本征能量、本征波函数、格点参与数,深入研究准周期调制势(λ)对扩展态、局域态和迁移率边的调控效应.结果表明,AAH马赛克晶格可同时存在扩展态、局域态和临界态,增大λ强度使得量子态由扩展态向局域态转变,同时改变迁移率边位置并相应减少扩展态状态数(N_(e))和扩大局域态状态数.进一步研究了AAH马赛克晶格中量子扩散,发现量子扩散始终具有弹道式运动形式,其中速率v与λ呈反比关系.通过迁移率边计算得到N_(e),发现N_(e)与λ同样呈反比关系.量子扩散速率与N_(e)对λ强度具有同样的依赖关系,表明系统中弹道式扩散来源于扩展态的贡献,N_(e)随λ增大而减少,进而导致量子扩散速率相应降低.研究结果将为调控弹道式量子扩散提供理论指导.Quantum diffusion in the one-dimensional quasi-periodic Aubry-André-Harper(AAH)mosaic lattice model is studied based on the tight-binding Hamiltonian framework.The modulation effect of the quasi-periodic modulation potential(λ)on the extended states,localized states and mobility edges in the model is deeply investigated by calculating the eigen-energy,eigen-wave function and lattice participation number of the system.The results show that extended states,localized states and critical states exist at the same time in the AAH mosaic lattice,and increasing theλstrength makes the quantum states shift from the extended states to the localized states,change the position of the mobility edges,shrink the number of extended states(N_(e))and expand the number of localized states accordingly.By investigating the quantum diffusion in the AAH mosaic lattice deeply,it is found that the quantum diffusion always has a ballistic motion,where the rate v is inversely proportional toλ.The N_(e)can be estimated from the positions of mobility edges which is found to be inversely proportional toλ.The ballistic quantum diffusion rate and N_(e)have the same dependence on theλstrength,indicating that the ballistic motion in the system originates from the contribution of the extended states.The N_(e)decreases with the increase ofλ,which leads to a corresponding decrease in the quantum diffusion rate.The results will provide the theoretical guidance for modulating ballistic quantum diffusion.

关 键 词：Anderson局域化 AAH模型 迁移率边 量子扩散 

分 类 号：O469[理学—凝聚态物理]