Complete ionization for a non-autonomous point interaction model in d = 2

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.

arXiv comment38 pages, 1 figure. Final version to appear on Comm. Math. Phys

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Cited by in corpus (2)

• A general review on the NLS equation with point-concentrated nonlinearity
• Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity