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

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 $\eta (t)$. We show that for generic $\eta (t)$, 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 $\eta (t)$. There are however exceptional, very non-generic $\eta (t)$, that do not lead to full ionization, which include rather simple explicit periodic functions. For these $\eta (t)$ the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator.

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