TY - GEN A1 - Nettesheim, Peter T1 - Second Order Transitions in Quantum-Classical Molecular Dynamics N2 - 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 Schrödinger 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. T3 - ZIB-Report - SC-98-37 KW - quantum-classical molecular dynamics KW - mixed quantum-classical models KW - asymptotics KW - quantum populations Y1 - 1998 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/380 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-3805 ER -