论文标题
一维不合命系统中局部扩展过渡的平面波研究
A plane wave study on the localized-extended transitions in the one-dimensional incommensurate systems
论文作者
论文摘要
基于我们最近提出的平面波框架，我们从理论上研究了具有余弦类型的电势的局部扩展的过渡，这些跃迁与超速原子和光子晶体的许多最新实验有着密切的联系。我们为在基态和单个粒子迁移率边缘的过渡中制定了基于繁殖的散射图片，其中揭示了不相差的电势，本征态组成和过渡机制之间的更深层次的联系。我们进一步表明，所有局部特征状态的本地化长度的上限都存在，从而导致与安德森本地化的根本差异。与分析一起介绍了数值计算，以证明我们的陈述是合理的。理论分析和数值方法也可以推广到具有不同电位或超越单个粒子状态的较高维度的系统，这将使相关领域的未来研究受益。
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent experiments in the ultracold atom and photonic crystal. We formulate a propagator based scattering picture for the transition at the ground state and single particle mobility edge, in which the deeper connection between the incommensurate potentials, eigenstate compositions and transition mechanism is revealed. We further show that there exists a upper limit of localization length for all localized eigenstates, leading to an fundamental difference to the Anderson localization. Numerical calculations are presented alongside the analysis to justify our statements. The theoretical analysis and numerical methods can also be generalized to systems in higher dimensions, with different potentials or beyond the single particle regime, which would benefit the future studies in the related fields.
