Published Paper

Inserted: 17 aug 2021
Last Updated: 4 oct 2022

Journal: Comm. Math. Phys.
Volume: 395
Number: 2
Pages: 963-1005
Year: 2022
Doi: https://doi.org/10.1007/s00220-022-04447-1

Abstract:

We consider the two dimensional Schrödinger equation with time dependent delta potential, 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 $\mathcal{O}((\log t /t)^2)$, up to lower order terms.