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arXiv · 1605.03520

An Egorov Theorem for avoided crossings of eigenvalue surfaces

Clotilde Fermanian Kammerer·Caroline Lasser
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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 Schroedinger 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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Clotilde Fermanian Kammerer, Caroline Lasser. 2016-05-11. An Egorov Theorem for avoided crossings of eigenvalue surfaces. https://doi.org/10.1007/s00220-017-2890-1

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