一种求解Escherfest动力学的有效时间分裂方法
An Efficient Time-splitting Method for the Ehrenfest Dynamics
摘要：
代表量子-经典平均场型耦合的Eschlafest动力学是量子分子动力学中广泛使用的近似。本文提出了一种时间分裂方法，用于求解非线性耦合薛定谔-刘维系统形式的Eschlafest动力学.我们证明了我们的分裂计划是稳定的一致的半经典参数，而且，它保持了一个离散的半经典极限。因此，人们可以使用仅由经典刘维尔方程引起的时间步长来精确地计算物理可观测量，即，独立的小半经典参数-除了经典的网格步长的刘维方程。数值算例验证了网格划分策略的有效性。
英文摘要：
The Ehrenfest dynamics, representing a quantum-classical mean-field type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a time-splitting method for an Ehrenfest dynamics, in the form of a nonlinearly coupled Schrödinger-Liouville system. We prove that our splitting scheme is stable uniformly with respect to the semiclassical parameter, and, moreover, that it preserves a discrete semiclassical limit. Thus one can accurately compute physical observables using time steps induced only by the classical Liouville equation, i.e., independent of the small semiclassical parameter - in addition to classical mesh sizes for the Liouville equation. Numerical examples illustrate the validity of our meshing strategy.
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