An Egorov Theorem for avoided crossings of eigenvalue surfaces
  We study nuclear propagation through avoided crossings of electron energy levels. We construct a surface hopping semigroup, which gives an Egorov-type description of the dynamics. The underlying time-dependent Schroedinger equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces have an avoided crossing. Using microlocal normal forms reminiscent of the Landau-Zener problem, we prove convergence to the true solution in the semi-classical limit. 
Clotilde Fermanian Kammerer, Caroline Lasser
math-ph math.AP math.MP