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→∞. 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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Received: 1 November 2000 / Accepted: 5 February 2001
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Costin, O., Costin, R., Lebowitz, J. et al. Evolution of a Model Quantum System¶ Under Time Periodic Forcing:¶Conditions for Complete Ionization. Commun. Math. Phys. 221, 1–26 (2001). https://doi.org/10.1007/s002200100455
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DOI: https://doi.org/10.1007/s002200100455