弹簧-质量机械系统拓扑相位和边缘模式的严格数学理论

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Ridvan Ozdemir, Junshan Lin
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引用次数: 0

摘要

在这项工作中,我们研究了当系统的空间反转对称性被打破时弹簧-质量点阵的拓扑相位,并证明了当两个拓扑相位不同的点阵粘合在一起时边缘模式的存在。特别是,对于由弹簧连接的无限质量阵列组成的一维网格,我们证明了网格的 Zak 相是量子化的,只取 0 或 π 值。对于二维蜂巢晶格,我们描述了当晶格顶点上的质量不均匀时晶格的谷切尔恩数。我们证明了将两个具有相反谷切尔恩数的半无限晶格粘合在一起所形成的联合蜂窝晶格存在边缘模式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems

In this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is quantized, only taking the value 0 or π. We also prove the existence of an edge mode when two semi-infinite lattices with distinct Zak phases are connected. For the two-dimensional honeycomb lattice, we characterize the valley Chern numbers of the lattice when the masses on the lattice vertices are uneven. The existence of edge modes is proved for a joint honeycomb lattice formed by gluing two semi-infinite lattices with opposite valley Chern numbers together.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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