经典映射模型在约束相空间中的双空间表示：开放量子系统的精确数值方法
Twin-Space Representation of Classical Mapping Model in the Constraint Phase Space Representation: Numerically Exact Approach to Open Quantum Systems
AI总结：
本文提出了一种基于双空间（TS）的相空间方法，用于精确描述开放量子系统的动力学，通过将减少系统的密度算符转换为具有双倍自由度的扩展系统的波函数，并利用经典映射模型将扩展系统的哈密顿量映射到其等效的经典模型上。
摘要：
约束坐标-动量相空间（CPS）最近被开发用于研究非绝热动力学在气相和凝聚相分子系统中。尽管CPS公式对于描述离散（电子/振动/自旋）状态自由度（DOFs）是精确的，但当研究凝聚相系统-环境模型时，以前的工作通常采用环境浴DOFs的离散化，这会破坏时间不可逆性，并可能使在长时间极限下获得数值收敛结果变得困难。在本文中，我们开发了一种精确的轨迹基相空间方法，通过采用量子统计力学的双空间（TS）公式，将减少系统的密度算符转换为具有两倍自由度的扩展系统的波函数。然后使用经典映射模型（CMM）将扩展系统的哈密顿量映射到其等效的经典模型上。为了证明TS-CMM方法的适用性，我们比较了几个基准凝聚相系统-环境模型的模拟人口动态和非线性光谱与通过层次方程方法获得的结果，表明我们的方法能够准确描述开放量子系统动力学。
英文摘要：
The constraint coordinate-momentum \textit{phase space} (CPS) has recently been developed to study nonadiabatic dynamics in gas-phase and condensed-phase molecular systems. Although the CPS formulation is exact for describing the discrete (electronic/ vibrational/spin) state degrees of freedom (DOFs), when system-bath models in condense phase are studied, previous works often employ the discretization of environmental bath DOFs, which breaks the time irreversibility and may make it difficult to obtain numerically converged results in the long-time limit. In this paper, we develop an exact trajectory-based phase space approach by adopting the twin-space (TS) formulation of quantum statistical mechanics, in which the density operator of the reduced system is transformed to the wavefunction of an expanded system with twice the DOFs. The classical mapping model (CMM) is then used to map the Hamiltonian of the expanded system to its equivalent classical counterpart on CPS. To demonstrate the applicability of the TS-CMM approach, we compare simulated population dynamics and nonlinear spectra for a few benchmark condensed phase system-bath models with those obtained from the hierarchical equations of motion method, which shows that our approach yields accurate dynamics of open quantum systems.
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