非绝热动力学自旋映射表示的电子路径积分简正模式
On the Electronic Path-Integral Normal Modes of the Spin-Mapping Representation of Nonadiabatic Dynamics
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中文总结 AI 辅助
本文研究自旋映射表示中电子路径积分简正模式，发现高模式受QBD约束，仅用质心即可复现N-珠子结果，实现守恒QBD的准确动力学，解释了自旋映射方法的近期成功。
中文摘要 AI 辅助
非绝热Matsubara动力学已在Meyer-Miller-Stock-Thoss（MMST）和自旋映射两种表示中被提出，其中动力学在核自由度的较高路径积分简正模式中被截断，但电子变量中不进行截断。与单表面Matsubara动力学相比，这些方法对于一般系统似乎不守恒量子玻尔兹曼分布（QBD）。最近的研究表明，在MMST表示的电子路径积分简正模式中进行截断，对于单条轨迹不会导致QBD的守恒，也无法准确计算关联函数。本文研究了自旋映射表示中的电子路径积分简正模式。我们关注一个二能级系统，尽管我们预期我们的发现适用于任意数量的电子态。我们或许令人惊讶地发现，自旋矢量z分量（即态布居数之差）的较高简正模式受到QBD的约束，时间演化的态布居数可观测量仅是自旋映射质心的函数，并且仅使用自旋映射质心即可复现完整的N-珠子计算结果，从而得到准确且守恒QBD的动力学。虽然目前这些结果尚不是一种普遍适用的方法，但我们相信这可能解释了近期自旋映射方法相对于MMST方法的成功，据我们所知，这是首个在电子简正模式截断中获得QBD守恒的方法，并将有助于未来推导高度准确且守恒量子玻尔兹曼的非绝热动力学方法。
英文摘要
Nonadiabatic Matsubara dynamics has been proposed in both the Meyer-Miller-Stock-Thoss (MMST) and spin-mapping representations, whereby the dynamics are truncated in the higher path-integral normal modes of the nuclear degrees of freedom, but no truncation is performed in the electronic variables. In contrast to single-surface Matsubara dynamics, these methods do not appear to conserve the Quantum Boltzmann Distribution (QBD) for general systems. Recently, it was shown that truncating in the electronic path-integral normal modes of the MMST representation does not lead to conservation of the QBD for a single trajectory or accurate computation of a correlation function. Here, the electronic path-integral normal modes in the spin-mapping representation are investigated. We focus on a two-level system although we expect our findings to be applicable to any number of electronic states. We find, perhaps surprisingly, that the higher normal modes of the spin-vector $z$-component, the difference in state populations, are constrained by the QBD, that the time-evolved state population observable is a function of only the spin-mapping centroid, and that the full $N$-bead computational results are replicated using only the spin-mapping centroid, leading to accurate, QBD conserving dynamics. While at present these results are not a generally-applicable method, we believe this may explain the recent success of spin-mapping approaches compared to MMST approaches, %To our knowledge, this is the first method obtaining conservation of the QBD when truncating in electronic normal modes and should aid the future derivation of highly accurate and Quantum Boltzmann conserving nonadiabatic dynamics methods.
发表机构
- University College London（伦敦大学学院）
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