Criticality in the Quantum Kicked Rotor with a Smooth Potential

Details Criticality in the Quantum Kicked Rotor with a Smooth Potential Criticality in the Quantum Kicked Rotor with a Smooth Potential

2008-08-13

arxiv.org/abs/0808.1783v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevE.78.031115

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.

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