Ionization for Three Dimensional Time-dependent Point Interactions

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 (α(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (α(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.

arXiv commentSome improvements and some references added, 26 pages, LaTeX

References in corpus (3)

• 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

Cited by in corpus (7)

• 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
• Microscopic Derivation of Time-dependent Point Interactions
• Complete ionization for a non-autonomous point interaction model in d = 2
• On the Atomic Photoeffect in Non-relativistic QED
• A general review on the NLS equation with point-concentrated nonlinearity
• Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity