We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called the spin partially linearized density matrix (spin-PLDM) approach. Within a classical trajectory picture, partially linearized methods treat the electronic dynamics along forward and backward paths separately by explicitly evolving two sets of mapping variables. Unlike previously derived partially linearized methods based on the Meyer–Miller–Stock–Thoss mapping, spin-PLDM uses the Stratonovich–Weyl transform to describe the electronic dynamics for each path within the spin-mapping space; this automatically restricts the Cartesian mapping variables to lie on a hypersphere and means that the classical equations of motion can no longer propagate the mapping variables out of the physical subspace. The presence of a rigorously derived zero-point energy parameter also distinguishes spin-PLDM from other partially linearized approaches. These new features appear to give the method superior accuracy for computing dynamical observables of interest when compared with other methods within the same class. The superior accuracy of spin-PLDM is demonstrated in this paper through application of the method to a wide range of spin-boson models as well as to the Fenna–Matthews–Olsen complex.

中文翻译：

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非绝热动力学的部分线性自旋映射方法。一，理论的推导

我们提出了一种新的基于部分线性化映射的方法，用于逼近凝聚相非绝热系统中的实时量子相关函数，称为自旋部分线性化密度矩阵（spin-PLDM）方法。在经典的轨迹图中，部分线性化方法通过显式演化两组映射变量来分别处理沿前向和后向路径的电子动力学。与先前基于Meyer-Miller-Stock-Thoss映射得出的部分线性化方法不同，spin-PLDM使用Stratonovich-Weyl变换来描述自旋映射空间内每个路径的电子动力学。这会自动将笛卡尔映射变量限制在一个超球面上，这意味着经典运动方程不再能够将映射变量传播到物理子空间之外。严格推导出的零点能量参数的存在也将自旋PLDM与其他部分线性化的方法区分开来。与同一类中的其他方法相比，这些新功能似乎为该方法提供了更高的计算动态感兴趣的动态观测值的准确性。通过将该方法应用于各种自旋玻色子模型以及Fenna-Matthews-Olsen络合物，证明了自旋PLDM的优越精度。与同一类中的其他方法相比，这些新功能似乎为该方法提供了更高的计算动态感兴趣的动态观测值的准确性。通过将这种方法应用于各种自旋玻色子模型以及Fenna-Matthews-Olsen复合体，证明了自旋PLDM的优越精度。与同类中的其他方法相比，这些新功能似乎为该方法提供了更高的计算动态感兴趣的动态观测值的准确性。本文通过将该方法应用于各种自旋玻色子模型以及Fenna–Matthews–Olsen复合体，证明了自旋PLDM的卓越准确性。