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 $\cO(1/\sqrt{E})$.