Seminari del Dipartimento
Analisi On the spectrum of the Schrödinger operator on d-dimensional tori: a normal form approach Beatrice Langella
26-06-2019 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - Aula 311
In this talk I will present a spectral result concerning unbounded perturbations of the Laplacian operator on an arbitrary flat torus T^d_Gamma obtained as the quotient of R^d with a maximal dimension lattice Gamma. By means of a normal form procedure based on pseudo-differential calculus, I will show how it is possible to obtain a full asymptotic expansion for most of the eigenvalues of such an operator (in particular, for a density one subset of its spectrum). Comparisons will be made with the one-dimensional case, enlightening the major difficulties related to the higher dimensional nature of the problem. Based on a joint work with Dario Bambusi and Riccardo Montalto |