Semiclassical asymptotics and gaps in the spectra of magnetic Schrödinger operators (Q1611628)

The authors study magnetic Schrödinger operators with invariant Morse type potentials on the covering space of a compact manifold. They adapt the \(L^2\) version of the semiclassical approximation due to Witten to establish the existence of spectral gaps for large values of the coupling parameter or equivalently for small values of the coupling constant. The physical explanation for the appearance of gaps in the spectrum is that the potential wells get deeper as \(\mu\rightarrow 0\) and the atoms get asymptotically isolated so that the energy levels are approximated by those of the corresponding model operator.