We consider the two dimensional Schrodinger equation with a time dependent point interaction, 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 O((log t /t)(2)), up to lower order terms.

Complete Ionization for a Non-autonomous Point Interaction Model in d = 2 / Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 395:2(2022), pp. 963-1005. [10.1007/s00220-022-04447-1]

Complete Ionization for a Non-autonomous Point Interaction Model in d = 2

Lorenzo Tentarelli
2022

Abstract

We consider the two dimensional Schrodinger equation with a time dependent point interaction, 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 O((log t /t)(2)), up to lower order terms.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2972041