Soffer, A.; Weinstein, M. I. Ionization and scattering for short-lived potentials. (English) Zbl 0930.35113 Lett. Math. Phys. 48, No. 4, 339-352 (1999). 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. Cited in 2 Documents 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 Keywords:perturbation; time-dependent resonance theory; scattering theory PDFBibTeX XMLCite \textit{A. Soffer} and \textit{M. I. Weinstein}, Lett. Math. Phys. 48, No. 4, 339--352 (1999; Zbl 0930.35113) Full Text: DOI