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Communications in Mathematical Physics

, Volume 353, Issue 3, pp 1011–1057 | Cite as

An Egorov Theorem for Avoided Crossings of Eigenvalue Surfaces

  • Clotilde Fermanian Kammerer
  • Caroline LasserEmail author
Article

Abstract

We study nuclear propagation through avoided crossings of electron energy levels. We construct a surface hopping semigroup, which gives an Egorov-type description of the dynamics. The underlying time-dependent Schrödinger equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces have an avoided crossing. Using microlocal normal forms reminiscent of the Landau–Zener problem, we prove convergence to the true solution in the semi-classical limit.

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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), UPEM, UPEC, CNRSCréteilFrance
  2. 2.Zentrum MathematikTechnische Universität MünchenMünchenGermany

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