| Quantum Accelerator Modes due to gravity have been discovered in experiments with cold atoms in periodically pulsed optical lattices. They are a purely quantal phenomenon, and yet have been explained in terms of stable periodic orbits of a formally classical dynamical system. This system emerges of a pseudoclassical limit, where the role of the Planck's constant is played by a parameter, that measures the offset from lowest-order resonances. In the case of higher-order resonances, no such limit exist. However, a pseudo-quasiclassical asymptotics on the quantum propagator, written as a sum over paths, still exposes ray dynamics: now rays come in families, belonging to different dynamical systems, each of which provides but a local approximation to quantum propagation. This result leads to prediction of new families of experimentally observable accelerator modes. |
|