Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori. (March 2022) - Bambusi, Dario; Langella, Beatrice; Montalto, Riccardo
Abstract: We study Schrödinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in λ − δ with δ ∈ ( 0, 1 ) for most of the eigenvalues λ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues). The proof is based on a structure theorem which is a variant of the one proved in [31, 32] and on a new iterative quasimode argument.