I will try to give an outline of some of the results obtained with Frederic 
during my PhD thesis concerning the semiclassical analysis of periodic 
media subject to exterior forces. Our goal has been to derive transport 
equations for periodic versions of Wigner transforms associated with 
oscillating solutions of a Schroedinger equation. A posteriori I can say 
that the main problems we had to face up have all been concerned with the 
crossings of energy levels and their possible interactions.