@misc{KubeWeber2006, author = {Kube, Susanna and Weber, Marcus}, title = {Coarse Grained Molecular Kinetics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9299}, number = {06-35}, year = {2006}, abstract = {The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.}, language = {en} } @misc{KubeLasserWeber2007, author = {Kube, Susanna and Lasser, Caroline and Weber, Marcus}, title = {Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9604}, number = {07-17}, year = {2007}, abstract = {Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.}, language = {en} }