Antiresonance and localization in quantum dynamics

The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for [Formula Presented] (a scaled [Formula Presented]) in the infinitesimal vicinity of QAR points [Formula Presented]. The localization length [Formula Presented] is determined from the analytical properties of the kicking potential. This "QAR localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly solvable cases, numerical evidence is given that QAR localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR localization to DL in a semiclassical strong-chaos regime, as [Formula Presented] is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.