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Resonances for the AC-Stark effect. (English) Zbl 0538.47010

Summary: The resonance problem for the AC-Stark effect is discussed. We prove that all bound states of the system \(-(1/2)\Delta +V(x)\) will turn into resonances after an AC-electric field is switched on and the order of the imaginary part of a resonance is determined by the number of the photons it takes to ionize the bound state which is turning into the resonance; if two bound states have energy difference of the photon, there exists a state which oscillates between the two states for a long time.

MSC:

47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators
47A10 Spectrum, resolvent
70K30 Nonlinear resonances for nonlinear problems in mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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