Resonances arising from unstable bound states: a
perturbative approach based on Mourre's inequality
(by Laura Cattaneo)
We consider the perturbation of bound states embedded in the continuous
spectrum which are unstable by the Fermi Golden Rule. The approach to
resonance theory based on spectral deformation by a 1-parameter
U(Ξ)=exp(iΞA) is extended to a more general class of quantum systems
characterized by Mourre's inequality and smoothness of the resolvent. Within
the framework of perturbation theory it is still possible to give an unambiguous
meaning to the notion of complex resonance energies and of corresponding
metastable states. The main result is a quasi-exponential decay estimate up
to a controlled error of higher order in the perturbation theory and a class of
operators for which it holds.