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

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

URL: http://arxiv.org/abs/2108.06564v4
Date: Tue, 28 Jun 2022 06:59:11 GMT
Title: Complete ionization for a non-autonomous point interaction model in d = 2
Authors: William Borrelli, Raffaele Carlone, Lorenzo Tentarelli
Abstract summary: We consider the two dimensional Schr"odinger equation with time dependent delta potential. We prove global well-posedness of the associated Cauchy problem. We investigate the behavior of the survival probability of a bound state of the time-independent problem.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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