Topology in Shallow-Water Waves: A Spectral Flow Perspective

Tauber, Clément; Thiang, Guo Chuan

doi:10.1007/s00023-022-01209-6

Cited by 7 publications

(1 citation statement)

References 30 publications

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“…These complications notwithstanding, the main lesson is clear: chiral modes observed in shallow water owe their existence to topology. Further studies of topological properties of the shallow water system can be found in [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A gauge theory for shallow water

Tong

2023

SciPost Phys.

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The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a d=2+1d=2+1 dimensional Abelian gauge theory. The magnetic field corresponds to the conserved height of the fluid, while the electric charge corresponds to the conserved vorticity. In a certain linearised approximation, the shallow water equations reduce to relativistic Maxwell-Chern-Simons theory. This describes Poincaré waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.

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Section: Introductionmentioning

confidence: 99%

A gauge theory for shallow water

Tong

2023

SciPost Phys.

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Spectral flow of fermions in the ℂP2 (anti-)instanton, and the sphaleron with vanishing topological charge

Amari,

Sawado,

Yamamoto

2024

J. High Energ. Phys.

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The spectral flow is ubiquitous in the physics of soliton-fermion interacting systems. We study the spectral flows related to a continuous deformation of background soliton solutions, which enable us to develop insight into the emergence of fermionic zero modes and the localization mechanism of fermion densities. We investigate a ℂP2 nonlinear sigma model in which there are the (anti-) instantons and also the sphalerons with vanishing topological charge. The standard Yukawa coupling of the fermion successfully generates infinite towers of the spectra and the spectral flow is observed when increasing the size of such solitons. At that moment, the localization of the fermions on the solitons emerges. The avoided crossings are also observed in several stages of the exchange of the flows, they are indicating a manifestation of the fermion exchange of the localizing nature.

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