论文标题
强烈非线性系统的拓扑不变和异常边缘模式
Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
论文作者
论文摘要
尽管对拓扑状态进行了广泛的研究，但它们在强烈的非线性古典系统中的表征仍缺乏。在这项工作中，我们确定了非线性散装模式的浆果相的适当定义，并在强烈非线性方向中的一维（1D）广义非线性schrödinger方程中表征了拓扑阶段。我们制定了一种分析策略，以证明由于反射对称性而导致的非线性浆果相的量化。模式振幅本身在非线性模式中起关键作用，并控制拓扑相变。然后，我们通过识别相关的非线性拓扑边缘模式来显示散装的对应关系。有趣的是，异常的拓扑模式从晶格边界衰减到受非线性固定点控制的高原。我们提出可以实现实施的被动光子和主动电气系统。我们的作品为物质和非线性动力学之间的丰富物理学打开了大门。
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize topological phases in one-dimensional (1D) generalized nonlinear Schrödinger equations in the strongly nonlinear regime. We develop an analytic strategy to demonstrate the quantization of nonlinear Berry phase due to reflection symmetry. Mode amplitude itself plays a key role in nonlinear modes and controls topological phase transitions. We then show bulk-boundary correspondence by identifying the associated nonlinear topological edge modes. Interestingly, anomalous topological modes decay away from lattice boundaries to plateaus governed by fixed points of nonlinearities. We propose passive photonic and active electrical systems that can be experimentally implemented. Our work opens the door to the rich physics between topological phases of matter and nonlinear dynamics.
