If anyone is interested in this paper:

"Manifestation of the topological index formula in quantum waves and geophysical waves" https://arxiv.org/pdf/1901.10592.pdf

> "Abstract: Using semi-classical analysis in R^n we present a quite general model for which the topological index formula of Atiyah-Singer predicts a spectral flow with a transition of a finite number of eigenvalues transitions between clusters (energy bands). This model corresponds to physical phenomena that are well observed for quantum energy levels of small molecules [9, 10] but also in geophysics for the oceanic or atmospheric equatorial waves [20, 4]."