Manifestation of the topological index formula in quantum waves and geophysical waves
Annales Henri Lebesgue, Volume 6 (2023), pp. 449-492.


Keywords PDEs in connection with geophysics, Molecular physics, K-theory, Fredholm operators, index theories, Semiclassical techniques


Using semi-classical analysis in 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 [FZ00, FZ01], also in geophysics for the oceanic or atmospheric equatorial waves [DMV17, Mat66] and expected to be observed in plasma physics [QF22].


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