02-186 Clotilde Fermanian-Kammerer, Caroline Lasser

Wigner measures and codimension two crossings (388K, ps.gz) Apr 15, 02

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Abstract. This paper gives a semiclassical description of nucleonic propagation through codimension two crossings of electronic energy levels. 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.

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