Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

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.