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Wigner Measure Propagation and Conical Singularity for General Initial Data

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Abstract

We study the evolution of Wigner measures of a family of solutions of a Schrödinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.

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Authors and Affiliations

  1. LAMA, UMR CNRS 8050, Université Paris-Est Créteil, 61, avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Clotilde Fermanian-Kammerer

  2. Université Paris-Sud, Mathématiques, Bat. 425, 91405, Orsay, France

    Patrick Gérard

  3. Zentrum Mathematik-M3, Wissenschaftliches Rechnen, Technische Universität München, 85747, Garching bei München, Germany

    Caroline Lasser

Authors
  1. Clotilde Fermanian-Kammerer
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  2. Patrick Gérard
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  3. Caroline Lasser
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Correspondence to Clotilde Fermanian-Kammerer.

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Communicated by A. Mielke

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Fermanian-Kammerer, C., Gérard, P. & Lasser, C. Wigner Measure Propagation and Conical Singularity for General Initial Data. Arch Rational Mech Anal 209, 209–236 (2013). https://doi.org/10.1007/s00205-013-0622-z

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  • DOI: https://doi.org/10.1007/s00205-013-0622-z

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