Clotilde Fermanian-Kammerer, Caroline Lasser
Wigner measures and codimension two crossings
(388K, ps.gz)

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.