Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case

TL;DR

This paper investigates how a three-dimensional quantum bound state evolves under a time-periodic interaction, proving complete ionization and scattering behavior over time under weak conditions.

Contribution

It provides a rigorous proof of complete ionization and scattering for a quantum system with a time-periodic zero-range interaction, under weak generic conditions.

Findings

Complete ionization as time approaches infinity.

All states become scattering states under the given conditions.

Proves results for weak generic Fourier coefficient conditions.

Abstract

We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength'' (\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t \to \infty). We prove also that, under the same conditions, all the states of the system are scattering states.