论文标题
改进的黄金规则率的路径综合法
An improved path-integral method for golden-rule rates
论文作者
论文摘要
我们提出了一种简单的方法，用于计算费米黄金规则极限中的反应速率，该方法准确地捕获了隧道和零点能的影响。该方法基于Thapa，Fang和Richardson最近提出的最近提出的黄金规范过渡状态理论（GR-QTST）的修改。尽管GR-QTST的大小不一致，但导致速率无界错误的可能性，但我们的修改方法没有这样的问题，因此可以可靠地应用于凝结的相系统。两种方法都涉及在受约束的集合中进行的路径综合采样。但是，这两种方法在选择约束功能方面有所不同。我们从数值上证明，对于Thapa和同事考虑的一维模型，我们的修改方法与GR-QTST一样准确。然后，我们研究了多维自旋 - 玻色子模型，为此，我们的方法准确地预测了真实的量子速率，而GR-QTST则随着光谱密度离散化而随着玻色子模式的增加而分解。我们的方法能够准确地预测MARCUS倒置政权中的反应速率，而无需Wolynes理论所需的分析延续。
We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunnelling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang and Richardson. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and coworkers. We then study a multi-dimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretisation of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime, without the need for the analytic continuation required by Wolynes theory.
