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

• URL: http://arxiv.org/abs/1901.10592v3
• Date: Sun, 24 Sep 2023 11:32:10 GMT
• Title: Manifestation of the topological index formula in quantum waves and geophysical waves
• Abstract summary: 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, also in geophysics for the oceanic or atmospheric equatorial waves and expected to be observed in plasma physics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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