How to correct Ehrenfest nonadiabatic dynamics in open quantum systems: Ehrenfest plus random force (E$+$$\sigma$) dynamics

TL;DR

This paper introduces E+σ dynamics, an improved Ehrenfest-based method that incorporates random forces to enhance accuracy in simulating open quantum systems while maintaining computational efficiency.

Contribution

The authors develop E+σ dynamics, adding random forces to Ehrenfest dynamics to improve accuracy in open quantum systems, applicable to both Markovian and non-Markovian cases.

Findings

E+σ accurately reproduces nonadiabatic dynamics in open systems.

The method satisfies detailed balance in various scenarios.

E+σ maintains high computational efficiency similar to Ehrenfest dynamics.

Abstract

One key challenge in the study of nonadiabatic dynamics in open quantum systems is to balance computational efficiency and accuracy. Although Ehrenfest dynamics (ED) is computationally efficient and well-suited for large complex systems, ED often yields inaccurate results. To address these limitations, we improve the accuracy of the traditional ED by adding a random force (E$+$$\sigma$). In this work, the construction of random forces is considered in Markovian and non-Markovian scenarios, and we ensure the dynamics satisfy the detailed balance in both scenarios. By comparing our E$+$$\sigma$ with existing methods such as the electronic friction model and surface hopping, we furthermore validate its reliability. In addition, E$+$$\sigma$ model still retains the high efficiency of the ED and does not incur much additional computation. We believe that this method provides an alternative to accurately describe mixed quantum-classical dynamics in open quantum systems, particularly for large complex systems.