In order to alleviate the computational costs of fully quantum nonadiabatic dynamics, we present a mixed quantum-classical (MQC) particle method based on the theory of Koopman wavefunctions. Although conventional MQC models often suffer from consistency issues such as the violation of Heisenberg's principle, we overcame these difficulties by blending Koopman's classical mechanics on Hilbert spaces with methods in symplectic geometry. The resulting continuum model enjoys both a variational and a Hamiltonian structure, while its nonlinear character calls for suitable closures. Benefiting from the underlying action principle, here we apply a regularization technique previously developed within our team. This step allows for a singular solution ansatz which introduces the trajectories of computational particles - the koopmons - sampling the Lagrangian classical paths in phase space. In the case of Tully's nonadiabatic problems, the method reproduces the results of fully quantum simulations with levels of accuracy that are not achieved by standard MQC Ehrenfest simulations. In addition, the koopmon method is computationally advantageous over similar fully quantum approaches, which are also considered in our study. As a further step, we probe the limits of the method by considering the Rabi problem in both the ultrastrong and the deep strong coupling regimes, where MQC treatments appear hardly applicable. In this case, the method succeeds in reproducing parts of the fully quantum results.

翻译：为降低全量子非绝热动力学的计算成本，我们提出一种基于Koopman波函数理论的混合量子-经典粒子方法。尽管传统混合量子-经典模型常存在一致性缺陷（如违反海森堡原理），我们通过将希尔伯特空间上的Koopman经典力学与辛几何方法相结合，克服了这些困难。所得连续模型兼具变分结构与哈密顿结构，而其非线性特性需要合适的闭合方案。得益于底层作用量原理，本文采用团队先前发展的正则化技术。该步骤允许引入奇异解拟设，从而产生计算粒子轨迹——即采样相空间中拉格朗日经典路径的koopmon。在Tully非绝热问题中，该方法重现了全量子模拟结果，其精度水平是标准混合量子-经典Ehrenfest模拟无法达到的。此外，与研究中对比的类似全量子方法相比，koopmon方法具有计算优势。作为进一步探索，我们通过考察超强耦合与深强耦合体系下的Rabi问题，测试了该方法的适用边界——这些区域通常难以应用混合量子-经典处理。在此情况下，该方法成功复现了部分全量子结果。