A Theory for Quantum Accelerator Modes in Atom Optics
  Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of a limit that is very similar to the semiclassical limit, but with a small parameter that is not Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity. 
Shmuel Fishman, Italo Guarneri, Laura Rebuzzini