Fast quantum, semiclassical and classical dynamics near the conical intersection

The dynamics of wavepacket propagation on a double circular 2-dimensional cone has been studied. The fast transition of the wavepacket from the conical well onto the conical peak is interpreted in terms of the semiclassical picture which uses the notion of the transition probability in the region of closest approach of the packet to the apex of the cone. It is shown that a simple surface hopping approximation predicts correctly the decay probability over times longer than the period of motion in the conical well.