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

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'' (α(t)). Under very weak generic conditions on the Fourier coefficients of (α(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.

arXiv commentLaTeX2e, 15 pages

References in corpus (4)

• Evolution of a model quantum system under time periodic forcing: conditions for complete ionization
• Decay versus survival of a localized state subjected to harmonic forcing: exact results
• Rotating Singular Perturbations of the Laplacian
• Ionization of a Model Atom: Exact Results and Connection with Experiment

Cited by in corpus (6)

• The point-like limit for a NLS equation with concentrated nonlinearity in dimension three
• Well-posedness of the Two-dimensional Nonlinear Schrödinger Equation with Concentrated Nonlinearity
• Two-dimensional Time-dependent Point Interactions
• Microscopic Derivation of Time-dependent Point Interactions
• Time dependent delta-prime interactions in dimension one
• An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions