论文标题
具有非本地反馈控制相互作用的非热弹性晶格的动力学和拓扑
Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
论文作者
论文摘要
我们研究以非本地反馈控制相互作用为特征的非热弹性晶格。在一维晶格中，我们表明比例控制相互作用会产生复杂的分散关系，其特征是相反的传播方向的增益和损失。取决于对照相互作用的非本地性质，由相反的非重新性行为为特征的多个频带中产生的非近代性发生。还研究了分散拓扑结构，重点是缠绕数量和非铁皮皮肤效应，这通过位于有限晶格边界的散装模式表现出来。在二维晶格中，非核心与方向依赖性波扩增有关。此外，非铁皮皮肤效应表现为位于有限晶格条边界上的模式，在有限的晶格条的边界上，其在两个方向上的综合效应导致存在位于有限的二维晶格角处的散装模式。我们的结果描述了非省弹性晶格的基本特性，以及开放的新可能性，用于设计具有与选择性波滤波，放大和定位有关的新功能的超材料。结果还表明，反馈相互作用可能是研究非富甲系统拓扑阶段的有用策略。
We investigate non-Hermitian elastic lattices characterized by non-local feedback control interactions. In one-dimensional lattices, we show that the proportional control interactions produce complex dispersion relations characterized by gain and loss in opposite propagation directions. Depending on the non-local nature of the control interactions, the resulting non-reciprocity occurs in multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is also investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional dependent wave amplification. Moreover, the non-Hermitian skin effect manifests as modes localized at the boundaries of finite lattice strips, whose combined effect in two directions leads to the presence of bulk modes localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and open new possibilities for the design of metamaterials with novel functionalities related to selective wave filtering, amplification and localization. The results also suggest that feedback interactions may be a useful strategy to investigate topological phases of non-Hermitian systems.
