Solving the Wigner equation for chemically relevant scenarios: Dynamics in 2D

The signed particle Monte Carlo (SPMC) approach has been used in the past to model steady-state and transient dynamics of the Wigner quasi-distribution for electrons in low-dimensional semiconductors. Here, we make a step toward high-dimensional quantum phase-space simulation in chemically relevant scenarios by improving the stability and memory demands of SPMC in 2D. We do so by using an unbiased propagator for SPMC to improve trajectory stability and applying machine learning to reduce memory demands for storage and manipulation of the Wigner potential. We perform computational experiments on a 2D double-well toy model of proton transfer and demonstrate stable pico-second-long trajectories that require only a modest computational effort.