@misc{Nettesheim1998, author = {Nettesheim, Peter}, title = {Second Order Transitions in Quantum-Classical Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3805}, number = {SC-98-37}, year = {1998}, abstract = {Mixed quantum--classical models have attracted considerable interest due to the expectation that they correctly describe non--adiabatic processes of full quantum dynamics. One of these models, the so--called QCMD model, represents most degrees of freedom of the molecular system by the means of classical mechanics but an important, small portion of the system is modeled by a wavefunction: the wavefunction is nonlinearly coupled to the classical motion via a singularly perturbed Schr{\"o}dinger equation. In extension to the analysis given by F.A.~Bornemann [{\em Homogenization in Time of Singularly Perturbed Mechanical Systems}, Lecture Notes in Mathematics, no.~1687, 1998, Springer, Berlin], the article presents an asymptotic expansion up to second order in the perturbation parameter. This result allows for the construction of new models and numerical integration schemes.}, language = {en} }