2006/08/16 by Ovidiu Costin, O. Costin, Rodica D. Costin +5
Mathematics · Physics and Astronomy · #81Q05 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:81Q05
paper · pdf · doi:10.48550/arxiv.math-ph/0608038
arxiv created 2006/08/16 · openalex publication_date 2006/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. We show that for generic forcing which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized for large t irrespective of the magnitude or frequency of the forcing. There are however exceptional, very non-generic forcings that do not lead to full ionization. These include rather simple explicit periodic forcings for which the system evolves to a nontrivial localized stationary state related to eigenfunctions of the Floquet operator.