Quantum transport on KAM tori

Although quantum tunneling between phase space tori occurs, it is suppresse d in the semiclassical limit (h) over bar SE arrow 0 for the Schrodinger eq uation of a particle in R-d under the influence of a smooth periodic potent ial. In particular this implies that the distribution of quantum group velocitie s near energy E converges to the distribution of the classical asymptotic v elocities near E, up to a term of the order O(1/root E).