Time evolution in a driven quantum system: Excitation through bands of states

Time-evolution patterns for energy absorption in a driven H\'enon-Heiles Hamiltonian with and without extra off-diagonal random-coupling terms are reported. The time dependence of the average number of photons absorbed is quite different for these two systems, being fluence dependent for the latter. Similarities are found between the dynamics of the driven system with random coupling and a four-mode molecular model which interacts with a quantum monochromatic field. Comparison is made between the presently found mechanism of excitation and the diffusive energy growth due to externally induced chaos found in the kicked-rotor or in microwave ionization of the hydrogen atom.