Decay of quantum accelerator modes

Experimentally observable quantum accelerator modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/h, are identified, depending on the resolution of KAM substructures that is achieved on the scale of h. The theory of resonance assisted tunneling introduced by Brodier [Ann. Phys. 300, 88 (2002)] is reexamined and found to well describe decay whenever applicable.