MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Quantum transport on KAM tori

Joachim Asch and Andreas Knauf


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


Related publications

1999 Repository Open Access
Joachim Asch and Andreas Knauf

Quantum transport on KAM tori

In: Communications in mathematical physics, 205 (1999) 1, pp. 113-128