Nonperturbative analysis of a model quantum system under time periodic forcing

TL;DR

This paper studies a quantum system with a time-varying potential, showing that generic periodic forcing causes full ionization over time, while specific non-generic forcings can lead to stable localized states.

Contribution

It provides a nonperturbative analysis of ionization in a quantum system under periodic forcing, identifying conditions for full ionization versus stable states.

Findings

Generic periodic forcing leads to full ionization.

Certain explicit forcings result in localized stationary states.

Full ionization occurs regardless of forcing magnitude or frequency.

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.