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：为缓解全量子非绝热动力学的高昂计算成本，本文提出一种基于Koopman波函数理论的混合量子-经典（MQC）粒子方法。尽管传统MQC模型常存在违背海森堡原理等一致性问题，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。由此得到的连续介质模型兼具变分结构与哈密顿结构，其非线性特性要求适当的封闭方案。基于底层作用量原理，我们应用了团队先前开发的正则化技术。该步骤引入奇异解假设，使得计算粒子轨迹——即Koopmon——得以描述相空间中拉格朗日经典路径的采样。针对Tully非绝热问题，该方法再现了全量子模拟的结果，其精度水平是标准MQC Ehrenfest模拟所无法达到的。此外，相较于本研究中同样考虑的全量子方法，Koopmon方法在计算上更具优势。作为进一步探索，我们通过考虑超强耦合与深强耦合机制下的Rabi问题检验了该方法的适用边界——这一场景下MQC处理方法通常难以适用。结果表明，该方法成功复现了部分全量子计算结果。