Numerical evaluation of orientation averages and its application to molecular physics.

In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modeling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely related to integration over two- or three-dimensional unit spheres, a common problem discussed in numerical analysis. The computational cost of the integration depends significantly on the quadrature method, making the selection of an appropriate method crucial for the feasibility of simulations.

Optimized sampling of mixed-state observables.

Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example, in ultrafast coherent control at finite temperatures, then one approach to approximate time-dependent observables is to sample the density operator by solving the Schrödinger equation for a set of wave functions with randomized phases. We show that, on average, random-phase wave functions perform well for ensembles with high mixedness, whereas at higher purities a deterministic sampling of the energetically lowest-lying eigenstates becomes superior.