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 wavefunctions. 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 type of transitions in the quantum kicked rotor, with a kicking strength well within 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.