How to correct Ehrenfest nonadiabatic dynamics in open quantum systems: Ehrenfest plus random force (E + <i>σ</i>) 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 + σ). 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 + σ with existing methods such as the electronic friction model and surface hopping, we furthermore validate its reliability. In addition, the E + σ model still retains the high efficiency of ED and does not incur much additional computation. We believe that this method provides an alternative to accurately describe the mixed quantum–classical dynamics in open quantum systems, particularly for large complex systems.