Solving the Wigner Equation for Chemically Relevant Scenarios: Dynamics in 2D

TL;DR

This paper advances 2D quantum phase-space simulations by enhancing the stability and reducing memory use of the Signed Particle Monte Carlo method, enabling efficient modeling of chemically relevant electron dynamics.

Contribution

It introduces an unbiased propagator and machine learning techniques to improve SPMC stability and memory efficiency in high-dimensional Wigner function simulations.

Findings

Achieved stable pico-second trajectories in 2D proton transfer models.

Reduced computational resources needed for Wigner potential handling.

Demonstrated applicability to chemically relevant scenarios.

Abstract

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 towards 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 by applying machine learning to reduce memory demands for storage and manipulation of the Wigner potential. We perform computational experiments on a 2D double-well toymodel of proton transfer and demonstrate stable pico-second-long trajectories that require only a modest computational effort.