Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces

Abstract

In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm for simulating nonadiabatic quantum dynamics at metal surfaces with a continuous spectrum. This method consists of a Monte-Carlo algorithm for sampling the initial wave packets on the phase space and a surface-hopping type stochastic time propagation scheme for the wave packets. We prove that to reach a certain accuracy threshold, the sample size required is independent of both the semiclassical parameter $\epsilon$ and the number of metal orbitals $N$, which makes it one of the most promising methods to study the nonadiabatic dynamics. The algorithm and its convergence properties are also validated numerically. Furthermore, we carry out numerical experiments including exploring the nuclei dynamics, electron transfer and finite-temperature effects, and demonstrate that our method captures the physics which can not be captured by classical surface hopping trajectories.

arXiv comment41 pages, 10 figures

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• Born-Oppenheimer Breakdown in Graphene
• Computing quantum dynamics in the semiclassical regime
• Mixed quantum-classical dynamics from the exact decomposition of electron-nuclear motion
• Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics
• Lindblad equation and its semi-classical limit of the Anderson-Holstein model

Cited by in corpus (2)

• Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
• Stochastic Schrödinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective