Prof. William Borrelli “Il problema di ionizzazione per equazioni di Schrödinger con interazione puntuale”

The dynamics of Schrödinger equations with point interactions (“delta potentials”) can be described in a quantitative way, beyond perturbative regimes. In this talk I will present known results concerning the following ionization problem: considering a time-dependent periodic point interaction, one is interested in the long-time dynamics for initial data corresponding to
eigenstates of the Hamiltonian at t = 0. The ionization phenomenon corresponds to the fact that it is expected that the survival probability of the solution in the initial state tends to zero along the evolution. This can be proved rigorously in the case under consideration, also
providing the exact decay rate in time. We will describe such results in dimension d = 1,2,3, with emphasis on d = 2, recently established in collaboration with R. Carlone (Unina) and L. Tentarelli (Polito).