Ionization for Three Dimensional Time-dependent Point Interactions

TL;DR

This paper proves that a three-dimensional quantum particle with a periodic, time-dependent point interaction at the origin undergoes complete ionization and scattering over time, under weak conditions on the interaction's Fourier coefficients.

Contribution

It establishes the occurrence of complete ionization and scattering for a quantum system with a time-dependent point interaction, extending understanding of quantum dynamics with periodic perturbations.

Findings

Complete ionization as time approaches infinity.

All states become scattering states under the given conditions.

Results hold for weak conditions on Fourier coefficients of the interaction strength.

Abstract

We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength'' of the interaction (\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\alpha(t)), we prove that there is complete ionization as (t \to \infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.