Ionization and scattering for short-lived potentials

Citation
A. Soffer et Mi. Weinstein, Ionization and scattering for short-lived potentials, LETT MATH P, 48(4), 1999, pp. 339-352
Citations number
12
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
LETTERS IN MATHEMATICAL PHYSICS
ISSN journal
0377-9017 → ACNP
Volume
48
Issue
4
Year of publication
1999
Pages
339 - 352
Database
ISI
SICI code
0377-9017(1999)48:4<339:IASFSP>2.0.ZU;2-S
Abstract
We consider perturbations of a model quantum system consisting of a single bound state and continuum radiation modes. In many problems involving the i nteraction of matter and radiation, one is interested in the effect of time -dependent perturbations. A time-dependent perturbation will couple the bou nd and continuum modes causing 'radiative transitions'. Using techniques of time-dependent resonance theory, developed in earlier work on resonances i n linear and nonlinear Hamiltonian dispersive systems, we develop the scatt ering theory of short-lived (O(t(-1-epsilon))) spatially localized perturba tions. For weak pertubations, we compute (to second order) the ionization p robability, the probability of transition from the bound state to the conti nuum 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.