Abstract
The quantum kicked rotor and the classical kicked rotor are both shown to have truncated L\'evy 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 $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\Elzxh}}}$0 in agreement with the correspondence principle.
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