Classical Kolmogorov-Arnol'd-Moser tori and cantori are found to act as barriers in the quantum dynamics of a kicked rotator. In their vicinity the asymptotic distribution decays exponentially. The penetration depth of a Kolmogorov-Arnol'd-Moser torus scales as 0.66 and the penetration probability as 2.5. Cantori can inhibit the diffusive growth of mean square displacements and thus act as barriers more drastically than in classical systems.
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Geisel et al. (1986) studied this question.
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