Hierarchical structures in the phase space and fractional kinetics: II. Immense delocalization in quantized systems

Anomalous transport due to Levy-type flights in quantum kicked systems is s tudied. These systems are kicked rotor and kicked Harper model. It is confi rmed for a kicked rotor that there exist special "magic" values of a contro l parameter of chaos K=K*=6.908 745... for which an essential increasing of a localization length is obtained. Functional dependence of the localizati on length on both parameter of chaos and quasiclassical parameter (h) over tilde is studied. We also observe immense delocalization of the order of 10 (9) for a kicked Harper model when a control parameter K is taken to be K*= 6.349 972. This "magic" value corresponds to special phase space topology i n the classical limit, when a hierarchical self-similar set of sticky islan ds emerges. The origin of the effect is of the general nature and similar i mmense delocalization as well as increasing of localization length can be f ound in other systems. (C) 2000 American Institute of Physics. [S1054-1500( 00)01401-4].