论文标题
绝热和非绝热限制中的绝热表面跳跃算法的渐近分析
Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits
论文作者
论文摘要
表面跳跃算法是一类重要的量子动力学模拟算法，用于非绝热动力学，通常在绝热表示中进行，该算法可能在存在不确定的绝热势能表面（PESS）和绝热耦合项的情况下分解。表面跳跃算法的另一个问题是难以捕获MARCUS（弱耦合/非绝热）制度中过渡速率的正确缩放。尽管可以通过利用绝热代表来规避第一个问题，但是在理论层面上通常缺乏绝热表面跳跃算法。我们考虑[fang，lu。多尺度模型。模拟。 16：4，1603-1622，2018]，并提供了Marcus制度中过渡速率的渐近分析，这证明了自旋波森模型的正确缩放。我们提出了两个保证一般电势的条件。在相反的（强耦合/绝热）制度中，我们得出了有趣的算法的渐近行为，有趣的是，这种算法与一种均值场描述相匹配。此处使用的技术可能会阐明针对其他基于糖尿病的算法的分析。
Surface hopping algorithms, as an important class of quantum dynamics simulation algorithms for non-adiabatic dynamics, are typically performed in the adiabatic representation, which can break down in the presence of ill-defined adiabatic potential energy surfaces (PESs) and adiabatic coupling term. Another issue of surface hopping algorithms is the difficulty in capturing the correct scaling of the transition rate in the Marcus (weak-coupling/non-adiabatic) regime. Though the first issue can be circumvented by exploiting the diabatic representation, diabatic surface hopping algorithms usually lack justification on the theoretical level. We consider the diabatic surface hopping algorithm proposed in [Fang, Lu. Multiscale Model. Simul. 16:4, 1603-1622, 2018] and provide the asymptotic analysis of the transition rate in the Marcus regime that justifies the correct scaling for the spin-boson model. We propose two conditions that guarantee the correctness for general potentials. In the opposite (strong-coupling/adiabatic) regime, we derive the asymptotic behavior of the algorithm that interestingly matches a type of mean-field description. The techniques used here may shed light on the analysis for other diabatic-based algorithms.
