Topology in Shallow-Water Waves: A Spectral Flow Perspective

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 an...

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Bibliographic Details
Published in:Annales Henri Poincaré 2023-01, Vol.24 (1), p.107-132
Main Authors: Tauber, Clément, Thiang, Guo Chuan
Format: Article
Language:English
Subjects:
Boundary conditions
Classical and Quantum Gravitation
Condensed Matter
Dynamical Systems and Ergodic Theory
Elementary Particles
Fluid dynamics
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical Physics
Mesoscopic Systems and Quantum Hall Effect
Physical simulation
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Shallow water
Singularities
Theoretical
Topological insulators
Topology
Water waves
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Summary: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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-022-01209-6