PROPAGATION OF COHERENT STATES THROUGH CONICAL INTERSECTIONS

We analyze the propagation of a wave packet through a conical intersection. This question was addressed for Gaussian wave packets in the 90s by George Hagedorn and we consider here a more general setting. We focus on the case of the Schr & ouml;dinger equation but our methods are general enough to be adapted to systems presenting codimension-2 crossings and to codimension-3 ones with specific geometric conditions. Our main theorem gives explicit transition formulas for the profiles when passing through a conical crossing point, including precise computation of the transformation of the phase. Its proof is based on a normal form approach combined with the use of superadiabatic projectors and the analysis of their degeneracy close to the crossing.