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arXiv · 2108.06564

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

William Borrelli·Raffaele Carlone·Lorenzo Tentarelli
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Abstract

We consider the two dimensional Schr\"odinger 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.

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William Borrelli, Raffaele Carlone, Lorenzo Tentarelli. 2021-08-14. Complete ionization for a non-autonomous point interaction model in d = 2. https://doi.org/10.1007/s00220-022-04447-1

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