Phase-space sampling of propagated wavefunctions

Abstract

We propose propagated Wigner sampling as a method for transitioning from quantum dynamics to more approximate mixed quantum–classical trajectories. The initial dynamics is propagated quantum mechanically until, at a suitable time, the Wigner function is calculated, sampled, and the remaining dynamics propagated by trajectory-based surface hopping. The approach exploits the Wigner phase-space representation and generalizes the Wigner sampling commonly used to generate initial conditions for trajectory dynamics to the more general case of arbitrary multi-state wavefunctions. The method is tested and evaluated on the one-dimensional Tully models. It is shown to afford an accurate representation of the dynamics, producing better results than standard surface hopping. We propose suitable strategies for generating trajectories from the quantum-derived Wigner function and discuss the scenarios in which this approach may prove useful in the context of non-adiabatic excited-state dynamics.