The quantum kicked rotor and the classical kicked rotor are both shown to have truncated Levy distributions in momentum space, when the classical phase space has accelerator modes embedded in a chaotic sea. The survival probability for classical particles at the interface of an accelerator mode and the chaotic sea has an inverse power-law structure, whereas that for quantum particles has a periodically modulated inverse power law, with the period of oscillation being dependent on Planck's constant. These logarithmic oscillations are a renormalization group property that disappears as (h) over bar-->o in agreement with the correspondence principle. [References: 29]
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