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Abstract: The quantum kicked rotor and the classical kicked rotor are both shown to have truncated Lévy 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 ħ → 0 in agreement with the correspondence principle.
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Stefancich, Marco; Allegrini, Paolo; Bonci, Luca; Grigolini, Paolo & West, Bruce J.Anomalous diffusion and ballistic peaks: A quantum perspective,
article,
June 1998;
[College Park, Maryland].
(https://digital.library.unt.edu/ark:/67531/metadc75417/:
accessed March 18, 2024),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT College of Arts and Sciences.