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Quantum Transport on KAM Tori

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Abstract:

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 ℝd 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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Authors and Affiliations

  1. CPT-CNRS, Luminy Case 907, F-13288 Marseille Cedex 9, France. E-mail: asch@cpt.univ-mrs.fr, France

    Joachim Asch

  2. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, Germany, Germany

    Andreas Knauf

Authors
  1. Joachim Asch
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  2. Andreas Knauf
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Received: 14 December 1998 / Accepted: 19 February 1999

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Asch, J., Knauf, A. Quantum Transport on KAM Tori. Commun. Math. Phys. 205, 113–128 (1999). https://doi.org/10.1007/s002200050670

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  • DOI: https://doi.org/10.1007/s002200050670

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