States of a dynamically driven spin. I. Quantum-mechanical model

‘‘Dynamical driving’’ means driving a system by another dynamical system, in contrast to driving by an external force (which acts on the system but is not acted upon by the system). The model consists of a localized spin driven by a polarized beam of spins. A remarkably complex variety of behaviors is possible as a result of the competition between the aligning effect of interaction with the beam and the precession due to the external magnetic field. The state of the localized spin can evolve from pure to mixed, or from mixed to pure, and its motion is characterized by an attractor. The final state of the driven spin is usually independent of its initial state, so the model provides an example of quantum-state preparation. These effects cannot be produced by a prescribed external force.