A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems

TL;DR

This paper introduces a novel surface hopping Gaussian beam method that efficiently solves high-dimensional high-frequency linear transport systems, combining stochastic surface hopping with Gaussian beams for improved accuracy and parallelizability.

Contribution

The paper presents a new hybrid numerical method that integrates surface hopping with Gaussian beams to handle multiple characteristic directions in high-dimensional transport problems.

Findings

Effective in high-dimensional quantum-classical Liouville equations

Parallelizable Monte Carlo algorithm

Accurate handling of multiple characteristic directions

Abstract

We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined with Gaussian beam method to deal with the multiple characteristic directions of the transport system in high dimensions. The Monte Carlo nature of the proposed algorithm makes it easy for parallel implementations. We validate the performance of the algorithms for applications on the quantum-classical Liouville equations.