TY - GEN A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics N2 - 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. T3 - ZIB-Report - 07-17 KW - Metropolis Monte Carlo KW - approximation KW - quadrature KW - oscillating functions Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9604 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Computation of equilibrium densities in metastable dynamical systems by domain decomposition T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 339 EP - 342 PB - AIP Conference Proceedings ER - TY - JOUR A1 - Kube, Susanna A1 - Weber, Marcus T1 - A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations JF - Journal of Chemical Physics Y1 - 2007 U6 - https://doi.org/10.1063/1.2404953 VL - 126 IS - 2 ER - TY - CHAP A1 - Weber, Marcus A1 - Kube, Susanna T1 - Robust Perron Cluster Analysis for Various Applications in Computational Life Science T2 - Computational Life Sciences Y1 - 2005 SP - 57 EP - 66 ER - TY - JOUR A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics JF - Journal of Computational Physics Y1 - 2008 U6 - https://doi.org/10.1016/j.jcp.2008.11.016 VL - 228 IS - 6 SP - 1947 EP - 1962 ER - TY - CHAP A1 - Kube, Susanna A1 - Weber, Marcus T1 - Preserving the Markov Property of Reduced Reversible Markov Chains T2 - Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008 Y1 - 2008 VL - 1048 SP - 593 EP - 596 ER - TY - JOUR A1 - Weber, Marcus A1 - Kube, Susanna A1 - Walter, Lionel A1 - Deuflhard, Peter T1 - Stable Computation of Probability Densities of Metastable Dynamical Systems JF - SIAM J. Multiscale Model. Simul. Y1 - 2007 VL - 6 IS - 2 SP - 396 EP - 416 ER -