@misc{LasserRoeblitz, author = {Lasser, Caroline and R{\"o}blitz, Susanna}, title = {Computing expectation values for molecular quantum dynamics}, issn = {1438-0064}, doi = {/10.1137/090770461}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11461}, number = {09-30}, abstract = {We compute expectation values for the solution of the nuclear Schr{\"o}dinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.}, language = {en} } @misc{KubeLasserWeber, 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}, 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} } @article{LasserRoeblitz2010, author = {Lasser, Caroline and R{\"o}blitz, Susanna}, title = {Computing expectation values for molecular quantum dynamics}, series = {SIAM Journal on Scientific Computing}, volume = {32}, journal = {SIAM Journal on Scientific Computing}, number = {3}, doi = {/10.1137/090770461}, pages = {1465 -- 1483}, year = {2010}, language = {en} } @article{KubeLasserWeber2008, author = {Kube, Susanna and Lasser, Caroline and Weber, Marcus}, title = {Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics}, series = {Journal of Computational Physics}, volume = {228}, journal = {Journal of Computational Physics}, number = {6}, doi = {10.1016/j.jcp.2008.11.016}, pages = {1947 -- 1962}, year = {2008}, language = {en} } @article{KenfackMarquardtKParamonovetal.2010, author = {Kenfack, Anatole and Marquardt, Falko and K. Paramonov, Gennadij and Barth, Ingo and Lasser, Caroline and Paulus, Beate}, title = {Initial-state dependence of coupled electronic and nuclear fluxes in molecules}, series = {Phys. Rev. A}, volume = {81}, journal = {Phys. Rev. A}, number = {5}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.81.052502}, pages = {052502}, year = {2010}, language = {en} }