Kolmogorov-Arnol'd-Moser Barriers in the Quantum Dynamics of Chaotic Systems

Abstract

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 ${\ensuremath{\hbar}}^{0.66}$ and the penetration probability as ${\ensuremath{\hbar}}^{2.5}$. Cantori can inhibit the diffusive growth of mean square displacements and thus act as barriers more drastically than in classical systems.