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Kicked atoms under a constant Stark or gravity field are investigated forexperimental setups with cold and ultra cold atoms. The parametric stability ofthe quantum dynamics is studied using the fidelity. In the case of a quantumresonance, it is shown that the behavior of the fidelity depends on arithmeticproperties of the gravity parameter. Close to a quantum resonance, the longtime asymptotics of the fidelity is studied by means of a {\empseudo-classical} approximation first introduced by Fishman {\em et al.} [J.Stat. Phys. {\bf 110}, 911 (2003)]. The long-time decay of fidelity arises fromthe tunneling out of pseudo-classical stable islands, and a simple ansatz isproposed which satisfactorily reproduces the main features observed innumerical simulations.

Fidelity for kicked atoms with gravity near a quantum resonance