We study the survival probability associated with a semi-classical matrix Shrodinger operator that models the predissociation of a general molecule in the Born-Oppenheimer approximation. We show that it is given by its usual time-dependent exponentia
l contribution, up to a reminder term that is exponentially small (in the semiclassical parameter) with arbitrarily large rate of decay. The result applies in any dimension, and in presence of a number of resonances that may tend to infinity as the semiclassical parameter tends to 0.
In this paper we study the influence of an electric field on a two dimen-sional waveguide. We show that bound states that occur under a geometrical deformation of the guide turn into resonances when we apply an electric field of small intensity havin
g a nonzero component on the longitudinal direction of the system. MSC-2010 number: 35B34,35P25, 81Q10, 82D77.
We study the resonance phenomena for time periodic perturbations of a Hamiltonian $H$ on the Hilbert space $L^2(mathbb R ^d)$. Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-How
land formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations.
