Communications in Mathematical Physics

, Volume 205, Issue 1, pp 113–128 | Cite as

Quantum Transport on KAM Tori

  • Joachim Asch
  • Andreas Knauf


Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit ћ ↘ 0 for the Schrödinger equation of a particle in 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 \(\mathcal{O}(1/\sqrt E )\).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Joachim Asch
    • 1
  • Andreas Knauf
    • 2
  1. 1.CPT-CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, France. E-mail: asch@cpt.univ-mrs.frFrance
  2. 2.Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, GermanyGermany

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