Multifractality in the kicked rotator

Multifractal wave functions appear in a wide range of systems intermediate between integrable and chaotic systems. Their properties can be described by a set of multifractal dimensions that can be extracted from the non-trivial scaling of their moments. In this communication, we present our results on the multifractality of wave functions at the Anderson transition. More particularly, we focus on the kicked rotator model with three incommensurate frequencies, which has been shown to exhibit a localization- delocalization transition with increasing kicking strength. This transition could even be probed experimentally in the atom-optics realization of the system. We also consider a one-parameter family of quantum maps displaying the whole range of intermediate spectral statistics and relate the multifractal dimensions to these spectral properties.