We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations.
Eigenstate Transitions, Duality, and Anomalous Diffusion in a Quasiperiodic Qi-Wu-Zhang Chern Insulator
Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院先进量子研究中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Key Laboratory of Multiscale Spin Physics, Ministry of Education（教育部多尺度自旋物理重点实验室）；Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）
Competing skin effect and quasiperiodic localization in the non-Hermitian Su-Schrieffer-Heeger chain: Reentrant delocalization, spectral topology destruction, and entanglement suppression
Ring-localized states, radial aperiodicity and quantum butterflies on a Cayley tree
我们提出了一种分析方法，基于一个真正的空间抽取计划，提取准确的特征值的宏观大的一组固定的本地化激发的凯莱树分形网络。在一个紧密结合的计划，我们利用上述方法来仔细检查网络的确定性变形的效果，首先通过最近邻跳变积分值的分层分布，然后通过径向Aubry Andre Harper准周期调制。随着世代指数的增加，膨胀的无环树结构主机将本征态固定在从最外层环扩散到样本大部分的外围站点上，类似于森林火灾的蔓延，照亮了一组可预测的站点，并使其余的站点未被点燃。可以精确地设计振幅包络的穿透深度。准周期调制产生迄今未报道的量子蝴蝶，这已被进一步研究通过计算本征态的参与比的倒数，和多重分形分析。最后讨论了该方案对光子分形波导网络的适用性。
