Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations

TL;DR

This paper introduces the MF-GQME method, combining mean field theory with master equations, to improve accuracy and efficiency in simulating nonadiabatic quantum dynamics in complex systems.

Contribution

It develops a non-perturbative, non-Markovian approach that enhances mean field theory with master equations, enabling accurate long-time quantum dynamics simulations at reduced computational cost.

Findings

MF-GQME outperforms direct mean field theory in accuracy.

Computational speed-ups of 10 to 100 times are achieved.

Method is effective across various nonadiabatic regimes.

Abstract

In this article we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.