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تسجيل مستخدم جديدComplete ionization for a non-autonomous point interaction model in d = 2
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We consider the two dimensional Schrodinger 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 $mathcal{O}(t^{-1})$, up to exponentially fast decaying terms.
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