Spinor dynamics of quantum accelerator modes near higher-order resonances

Quantum accelerator modes were discovered in experiments with kicked cold atoms in the presence of gravity. They were shown to be tightly related to resonances of the quantum kicked rotor. In this paper a spinor formalism is developed for the analysis of modes associated with resonances of arbitrary order q >= 1. Decoupling of spin variables from the orbital ones is achieved by means of an ansatz of the Born-Oppenheimer type that generates q independent band dynamics. Each of these is described, in classical terms, by a map, and the stable periodic orbits of this map give rise to quantum accelerator modes, which are potentially observable in experiments. The arithmetic organization of such periodic orbits is briefly discussed.