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Ionization and scattering for short-lived potentials. (English) Zbl 0930.35113

Summary: We consider perturbations of a model quantum system consisting of a single bound state and continuum radiation modes. In many problems involving the interaction of matter and radiation, one is interested in the effect of time-dependent perturbations. A time-dependent perturbation will couple the bound and continuum modes causing ‘radiative transitions’. Using techniques of time-dependent resonance theory, developed in earlier work on resonances in linear and nonlinear Hamiltonian dispersive systems, we develop the scattering theory of short-lived \(({\mathcal O}(t^{-1-\varepsilon}))\) spatially localized perturbations. For weak perturbations, we compute (to second-order) the ionization probability, the probability of transition from the bound state to the continuum states. These results can also be interpreted as a calculation, in the paraxial approximation, of the energy loss resulting from wave propagation in a waveguide in the presence of a localized defect.

MSC:

35P05 General topics in linear spectral theory for PDEs
81U10 \(n\)-body potential quantum scattering theory
47N50 Applications of operator theory in the physical sciences
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