Wigner measures and codimension two crossings

This article 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 Schrödinger 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.