标题： 浅水波中的拓扑：谱流视角 显示英文标题

标题： Topology in shallow-water waves: A spectral flow perspective

摘要： 在拓扑绝缘体的背景下，最近发现浅水模型表现出异常的体边对应关系。 对于具有边界的模型，参数空间同时涉及纵向动量和边界条件，并表现出一种奇特的奇异性。 我们通过定义一种新的边缘指标来解决这个问题，该指标是围绕这个奇异性周围的谱流。 至关重要的是，这个边缘指标采样了一组完整的边界条件，我们将其解释为边界驱动的量子泵浦。 由于谱流的拓扑性质，我们的边缘指标是稳定的，我们利用散射理论和Levinson定理的相对版本证明了它与体Chern数指标的对应关系。 还研究了该模型的完整谱流结构。 显示英文摘要

摘要： In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary conditions, and exhibits a peculiar singularity. We resolve the anomaly in question by defining a new kind of edge index as the spectral flow around this singularity. Crucially, this edge index samples a whole family of boundary conditions, and we interpret it as a boundary-driven quantized pumping. Our edge index is stable due to the topological nature of spectral flow, and we prove its correspondence with the bulk Chern number index using scattering theory and a relative version of Levinson's theorem. The full spectral flow structure of the model is also investigated.