2000/11/01 by O. Costin, R. D. Costin, J. L. Lebowitz +1 · 3 citations
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:34L40 #msc:81Q05
paper · pdf · doi:10.1007/s002200100455
arxiv created 2000/11/01 · openalex publication_date 2001/01/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · 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 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.