SC 98-37 Peter Nettesheim: Second Order Transitions in Quantum-Classical Molecular
Dynamics
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 Schrödinger 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
MSC: 81Q20, 41A60