Manifestation of the topological index formula in quantum waves and geophysical waves (Q6093071)

The author using semi-classical analysis in \(\mathbb{R}^{n}\) presents a 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 [the author and \textit{B. Zhilinskii}, Lett. Math. Phys. 55, No. 3, 219--238 (2001; Zbl 0981.81028); Phys. Rev. Lett., 85, No. 5, 960--963 (2000; \url{doi:10.1103/PhysRevLett.85.960})], also in geophysics for the oceanic or atmospheric equatorial waves [\textit{P. Delplace} et al., Science 358, No. 6366, 1075--1077 (2017; Zbl 1404.86016); J. Meteorol. Soc. Jpn. Ser. II, 44, No. 1, 25--43 (1966)] as mentioned by the author.