Criticality in the quantum kicked rotor with a smooth potential

We investigate the possibility of an Anderson-type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wave functions. Our results show the typical characteristics of a critical behavior, i.e., multifractal eigenfunctions and a scale-invariant level statistics at a critical kicking strength which classically corresponds to a mixed regime. This indicates the existence of a localization to delocalization transition in the quantum kicked rotor. Our study also reveals the possibility of other types of transition in the quantum kicked rotor, with a kicking strength well within the strongly chaotic regime. These transitions, driven by the breaking of exact symmetries, e.g., time reversal and parity, are similar to weak-localization transitions in disordered metals.