Nonperturbative analysis of a model quantum system under time periodic forcing
Mathematical Physics
2007-05-23 v1 math.MP
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. 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.
Cite
@article{arxiv.math-ph/0608038,
title = {Nonperturbative analysis of a model quantum system under time periodic forcing},
author = {O. Costin and R. D. Costin and A. Rokhlenko J. Lebowitz},
journal= {arXiv preprint arXiv:math-ph/0608038},
year = {2007}
}