For a Wigner-Weisskopf model of an atom consisting of a
quantum dot coupled to an energy reservoir described by a
three-dimensional Laplacian we study 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. This is joint work with
H.K. Knörr, A. Jensen and G. Nenciu. Available online here :
https://arxiv.org/abs/1612.02354