  We study an analog of the classical Arnol'd diffusion in a quantum system of
two coupled non-linear oscillators one of which is governed by an external
periodic force with two frequencies. In the classical model this very weak
diffusion happens in a narrow stochastic layer along the coupling resonance,
and leads to an increase of total energy of the system. We show that the
quantum dynamics of wave packets mimics, up to some extent, global properties
of the classical Arnol'd diffusion. This specific diffusion represents a new
type of quantum dynamics, and may be observed, for example, in 2D semiconductor
structures (quantum billiards) perturbed by time-periodic external fields.
