非绝热动力学的部分线性自旋映射方法。I.理论推导
A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory
摘要：
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关联函数，称为自旋PLDM。在一个经典的轨迹图片，部分线性化的方法处理沿向前和向后的路径分别明确发展两套映射变量的电子动力学。与先前基于Meyer-Miller-Stock-Thoss映射的部分线性化方法不同，自旋PLDM使用Stratonovich-Weyl变换来描述自旋映射空间内每条路径的电子动力学;这自动限制了笛卡尔映射变量位于超球面上，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。严格推导的零点能量参数的存在也区分自旋PLDM从其他部分线性化的方法。这些新的功能似乎给该方法优越的精度计算动态可观的利益，与其他方法相比，在同一类。本文通过将该方法应用于广泛的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。
英文摘要：
We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM. 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 within this paper through application of the method to a wide range of spin-boson models, as well as to the Fenna-Matthews-Olsen complex.
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