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The coupling of orbital and spin degrees of freedom is the source of many interesting phenomena. Here, we study the electron dynamics in a quantum billiard driven by a periodic electric field-a mesoscopic rectangular quantum dot-with spin-orbit coupling. We find that the spatial and temporal profiles of the observables demonstrate the transition to chaotic dynamics with qualitative modifications of the power spectra and patterns of probability and spin density. The time dependence of the wavefunctions and spin density indicates spin-charge separation seen in the decay of the spin-charge density correlators. Experimental verification of this spin chaos effect can lead to a better understanding of the interplay between spin and spatial degrees of freedom in mesoscopic systems.

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that 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.

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