Exponential decay and resonances in a driven system

Abstract

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-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations.

16 pages