Quantum Transport on KAM Tori
arXiv:math-ph/9812006 · doi:10.1007/s002200050670
Abstract
Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit for the Schrödinger equation of a particle in $\bR^d$ under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy converges to the distribution of the classical asymptotic velocities near , up to a term of the order $\cO(1/\sqrt{E})$.
21 pages