Criticality in the Quantum Kicked Rotor with a Smooth Potential

Abstract

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.

15 figures, to be published in Physical review E, 2008

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Cited by in corpus (5)

• Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio
• Disorder perturbed Flat Bands II: a search for criticality
• Barrier induced chaos in kicked rotor : classical sub-diffusion and quantum localization
• Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
• Floquet states of kicked particle in a singular potential: Exponential and power-law profiles