Joachim Asch and Andreas Knauf
Quantum Transport on KAM Tori
(259K, postscript)

ABSTRACT.  Although quantum tunneling between phase space tori occurs, 
it is suppressed in the semiclassical limit $\hbar\searrow 0$ 
for the Schr\"{o}dinger 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 $E$ 
converges to the distribution of the classical asymptotic velocities 
near $E$, up to a term of the order $\cO(1/\sqrt{E})$.