Dynamique moléculaire de la prédissociation

We study the survival amplitude associated with a semiclassical matrix Schrödinger 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 exponential contribution, up to a reminder term that is small relative to the semiclassical parameter, and for which we find the main contribution. The result applies in any dimension, and in the presence of a number of resonances that may tend to infinity as the semiclassical parameter tends to 0.