Quantum Arnol'd diffusion in a rippled waveguide

We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the diffusion-like motion occurs for a particle in the region corresponding to a stochastic layer surrounding the coupling resonance. The rate of the quantum diffusion turns out to be less than the corresponding classical one, thus indicating the influence of quantum coherent effects. Another result is that even in the case when such a diffusion is possible, it terminates in time due to the mechanism similar to that of the dynamical localization. The quantum Arnol'd diffusion represents a new type of quantum dynamics, and may be experimentally observed in measurements of a conductivity of low-dimensional mesoscopic structures.