Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics
Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics
复制标题
量子经典分子动力学时间分割方案的可观测误差界
DOI：
10.1137/21m1462349
复制
发表时间：
2023
影响因子：
2.9
通讯作者：
Vilanova, Albert Tres
中科院分区：
文献类型：
--
作者：
Fang, Di;Vilanova, Albert Tres
量子经典分子动力学作为全量子薛定谔方程的部分经典极限，是量子分子动力学的一个广泛应用的框架。基本方程本质上是非线性的，包含一个量子部分(代表电子)和一个经典部分(代表原子核)。波函数的准确模拟通常需要与重新标度的普朗克常数相当的时间步长，从而导致在以下情况下的巨大成本。基于半经典分析，我们证明了所提出的时间分裂方案的Schwartz可观测量的一个附加可观测误差界，该误差界随着时间的减小而减小。此外，我们建立了一个一致的可观测误差界，它允许一个时间步长来准确地捕获物理可观测量，而不考虑其大小。数值结果验证了我们的估计。
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schrödinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum part (representing the electrons) and a classical part (standing for the nuclei). An accurate simulation of the wave function typically requires a time step comparable to the rescaled Planck constant, resulting in a formidable cost when. We prove an additive observable error bound of Schwartz observables for the proposed time-splitting schemes based on semiclassical analysis, which decreases asbecomes smaller. Furthermore, we establish a uniform-in-observable error bound, which allows for antime step to accurately capture the physical observable regardless of the size of. Numerical results verify our estimates.