The experimental study of cold atoms kicked by a pulsed optical standing wave and falling under gravity has led to the important discovery of the accelerator modes (QAMs). It is shown that QAMs in the absence of gravity can feature a rotational quasiregularity which cannot be found in the usual QAMs. Thus, QAMs with non-accelerating quasiregular segments may be used to control the quantum motion of atoms in a way which is not possible in the presence of gravity. Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved.

The existence of rotating accelerator-mode islands (RAIs), performing quasiregular motion in rotational resonances of order m > 1 of the standard map, is firmly established by an accurate numerical analysis of all the known data. It is found that many accelerator-mode islands for relatively small nonintegrability parameter K are RAIs visiting resonances of different orders m < or = 3. For sufficiently large K, one finds also "pure" RAIs visiting only resonances of the same order, m = 2 or m = 3. RAIs, even quite small ones, are shown to exhibit sufficient stickiness to produce an anomalous chaotic transport. The RAIs are basically different in nature from accelerator-mode islands in resonances of the "forced" standard map which was extensively studied recently in the context of quantum accelerator modes.

A detailed characterization of stability islands in area-preserving maps is introduced on the basis of the resonance partition of phase space and it is used to define chaotic stickiness in these maps. It is shown that a general island can be characterized by a well-defined quasiregularity "type," specifying the sequence of resonances visited by the island. In particular, a "tangle" island lies entirely not just within the turnstile lobe of a resonance but also within the turnstile overlap of two resonances. Chaotic stickiness to a given island is then defined as the coincidence of the type of a chaotic orbit with that of the island in some time interval. This definition allows one to study stickiness systematically on all time scales, including short or nonasymptotic time regimes, as illustrated in the case of an accelerator-mode island of the standard map. A physically significant identification of the "sticky layer" and its "sublayers" in this case is made and discussed.