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MiS Preprint
56/1998
Quantum transport on KAM tori
Joachim Asch and Andreas Knauf
Abstract
Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit $h \searrow 0$ for the Schrödinger equation of a particle in $\mathbb{R}^d$ under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy E converges to the distribution of the classical asymptotic velocities near E, up to a term of the order $O(1/\sqrt{E} )$.
