论文标题
浅水波中的拓扑：违反散装对应关系
Topology in shallow-water waves: a violation of bulk-edge correspondence
论文作者
论文摘要
我们研究了描述地球海洋层的二维旋转浅水模型。它正式类似于Schrödinger方程，其中拓扑绝缘体的工具与之相关。一旦通过奇异的术语将小规模正规化，这种模型具有明确定义的散装指数。但是，在存在尖锐的边界的情况下，边缘模式的数量取决于边界条件，显示出明确违反批量边缘对应关系。我们研究了具有丰富相图的连续边界条件家族，并解释了此不匹配的起源。我们的方法依赖于散射理论和莱文森的定理。由于那里的散射幅度的分析结构，后者不适用于无限动量，最终是违规的原因。
We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schrödinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an odd-viscous term, such a model has a well-defined bulk topological index. However, in presence of a sharp boundary, the number of edge modes depends on the boundary condition, showing an explicit violation of the bulk-edge correspondence. We study a continuous family of boundary conditions with a rich phase diagram, and explain the origin of this mismatch. Our approach relies on scattering theory and Levinson's theorem. The latter does not apply at infinite momentum because of the analytic structure of the scattering amplitude there, ultimately responsible for the violation.
