Second Order Transitions in Quantum-Classical Molecular Dynamics
Please always quote using this URN: urn:nbn:de:0297-zib-3805
- 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.
Author: | Peter Nettesheim |
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Document Type: | ZIB-Report |
Tag: | asymptotics; mixed quantum-classical models; quantum populations; quantum-classical molecular dynamics |
MSC-Classification: | 41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] |
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods | |
Date of first Publication: | 1998/12/21 |
Series (Serial Number): | ZIB-Report (SC-98-37) |
ZIB-Reportnumber: | SC-98-37 |