Second Order Transitions in Quantum-Classical Molecular Dynamics

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 quantum wavefunction: the wavefunction is nonlinearly coupled to the classical motion via a singularly perturbed Schrodinger equation. In extension to the analysis given by F.A. Bornemann [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. Keywords: quantum--classical molecular dynamics; mixed quantum--classical models; asymptotics; quantum populations MS..