Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

TL;DR

This paper introduces an improved method combining quantum master equations with surface hopping to enable accurate, long-time nonadiabatic quantum dynamics simulations of complex systems, overcoming previous computational limitations.

Contribution

It presents a novel approach that enhances the efficiency and accuracy of surface hopping methods for long-time nonadiabatic quantum dynamics.

Findings

Method is numerically exact in certain regimes.

Outperforms fewest-switches surface hopping and mean field approaches.

Enables long-time simulations of complex quantum systems.

Abstract

The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing to unfavorable numerical scaling. In this paper we show that this problem can be alleviated by combining it with a formally exact generalized quantum master equation treatment. This allows dramatic improvements in the efficiency of the approach in nonadiabatic regimes, making it computationally tractable to treat the quantum dynamics of complex systems for long times. We demonstrate our approach by applying it to a model of condensed phase charge transfer where our method is shown to be numerically exact in regimes where fewest-switches surface hopping and mean field approaches fail to obtain the either the correct rates or long-time populations.