Critical metastability and destruction of the splitting in non-autonomous systems

We study a periodically driven double well model. As in the case of autonomous models. previously treated in a joint paper with A. Martinez, ((7)) we have the destruction of the splitting for critical metastability. The relevance of the model for the understanding of the red shift in the inversion line of the molecule of ammonia is shortly discussed. We show that, in order to have a reasonable behavior of the metastability as a function of the frequency, a non-monochromatic perturbation is needed.