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Evolution of a model quantum system under time periodic forcing: conditions for complete ionization

O. Costin·R. D. Costin·J. L. Lebowitz·A. Rokhlenko
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Abstract

We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $η(t)$. We show that for generic $η(t)$, which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized as $t\to\infty$. This is irrespective of the magnitude or frequency (resonant or not) of $η(t)$. There are however exceptional, very non-generic $η(t)$, that do not lead to full ionization, which include rather simple explicit periodic functions. For these $η(t)$ the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator.

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O. Costin, R. D. Costin, J. L. Lebowitz, A. Rokhlenko. 2000-11-01. Evolution of a model quantum system under time periodic forcing: conditions for complete ionization. https://doi.org/10.1007/s002200100455

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