Clotilde FERMANIAN KAMMERER
Wigner Measures and Molecular Propagation through Generic Energy Level Crossings
(614K, Postscript)
ABSTRACT. We study time-dependant Schr dinger equation with matrix-valued potential presenting some generic crossing of type B, I, J or K in Hagedorn's classification. We use two-scale Wigner measures for calculating the Landau-Zener energy transfer which occurs at the crossing. Our method provides a unified framework in which codimension 2, 3 or 5 crossings can be discussed. We recover Hagedorn's result for wave packets, from Wigner measure point of view, and extend them to any data uniformly bounded in the space of square integrable functions. The proof is based on a normal form theorem which reduces the problem to an operator-valued Landau-Zener formula.