标题： 绝热和非绝热极限下二面体表面跳跃算法的渐近分析 显示英文标题

标题： Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits

摘要： 表面跳跃算法作为一种重要的非绝热动力学模拟算法，通常在绝热表示中进行，这在存在定义不明确的绝热势能面（PES）和绝热耦合项时可能会失效。 表面跳跃算法的另一个问题是难以在Marcus（弱耦合/非绝热）区域中捕捉到跃迁速率的正确尺度。 尽管通过利用非绝热表示可以绕过第一个问题，但非绝热表面跳跃算法通常在理论上缺乏依据。 我们考虑了[Fang, Lu. Multiscale Model. Simul. 16:4, 1603-1622, 2018]中提出的非绝热表面跳跃算法，并提供了在Marcus区域中跃迁速率的渐近分析，这为自旋-玻色模型的正确尺度提供了理论依据。 我们提出了两个条件，以保证一般势能的正确性。 在相反的（强耦合/绝热）区域，我们推导了该算法的渐近行为，有趣的是，这与一种平均场描述相匹配。 这里使用的技术可能有助于其他基于非绝热的算法的分析。 显示英文摘要

摘要： 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.