- 02-186 Clotilde Fermanian-Kammerer, Caroline Lasser
- Wigner measures and codimension two crossings
Apr 15, 02
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Abstract. This paper gives a semiclassical description of
nucleonic propagation through codimension two crossings of electronic
Codimension two crossings are the simplest energy level crossings,
which affect the Born-Oppenheimer approximation in the zeroth order term.
The model we study is a two-level Schr\"odinger equation with a
Laplacian as kinetic operator and a matrix-valued linear potential,
whose eigenvalues cross, if the two nucleonic coordinates equal zero.
We discuss the case of well-localized initial data and obtain a description
of the wavefunction's two-scaled Wigner measure and of the weak limit of
its position density, which is valid globally in time.