  We consider a reduced two-channel model of an atom consisting of a quantum
dot coupled to an open scattering channel described by a three-dimensional
Laplacian. We are interested in the survival probability of a bound state when
the dot energy varies smoothly and adiabatically in time. The initial state
corresponds to a discrete eigenvalue which dives into the continuous spectrum
and re-emerges from it as the dot energy is varied in time and finally returns
to its initial value. Our main result is that for a large class of couplings,
the survival probability of this bound state vanishes in the adiabatic limit.
At the end of the paper we present a short outlook on how our method may be
extended to cover other classes of Hamiltonians; details will be given
elsewhere.
