Complete Ionization for a Non-autonomous Point Interaction Model in d = 2

We consider the two dimensional Schrödinger equation with a time dependent point interaction, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength varies in time. First, we prove global well-posedness of the associated Cauchy problem under general assumptions on the potential and on the initial datum. Then, for a monochromatic periodic potential (which also satisfies a suitable no-resonance condition) we investigate the asymptotic behavior of the survival probability of a bound state of the time-independent problem. Such probability is shown to have a time decay of order O((log t/ t) 2) , up to lower order terms.