Localization and fluctuations in quantum kicked rotors

We address the issue of fluctuations, about an exponential line shape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical locali zation. An exact renormalization scheme establishes the fractal character o f the fluctuations and provides a method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuati ons are independent of the kicking parameter k and exhibit self-similarity for certain values of the quasienergy. For given k,the asymptotic localizat ion length is a good characteristic of the localized line shapes for all qu asienergies. This is in stark contrast to the quadratic rotor, where the fl uctuations depend upon the strength of the kicking and exhibit local "reson ances." These resonances result in strong deviations of the localization le ngth from the asymptotic value. The consequences are particularly pronounce d when considering the time evolution of a packet made up of several quasie nergy states. [S1063-651X(99)09807-4].