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arXiv · 1901.10592

Manifestation of the topological index formula in quantum waves and geophysical waves

Frédéric Faure
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Abstract

Using semi-classical analysis in $\mathbb{R}^{n}$ we present a quite general model for which the topological index formula of Atiyah-Singer predicts a spectral flow with the transition of a finite number of eigenvalues between clusters (energy bands). This model corresponds to physical phenomena that are well observed for quantum energy levels of small molecules [faure_zhilinskii_2000,2001], also in geophysics for the oceanic or atmospheric equatorial waves [Matsuno_1966, Delplace_Marston_Venaille_2017] and expected to be observed in plasma physics [Qin, Fu 2022].

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Frédéric Faure. 2019-01-29. Manifestation of the topological index formula in quantum waves and geophysical waves. https://arxiv.org/abs/1901.10592

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