论文标题
关于基于Floquet的量子经典Liouville方程和表面跳跃的适当推导，描述了分子或材料受外部场的影响
On the Proper Derivation of the Floquet-based Quantum Classical Liouville Equation and Surface Hopping Describing a Molecule or Material Subject to an External Field
论文作者
论文摘要
我们研究了两种用于激光驱动的电子核动力学的适当基于Floquet的量子古典Liouville方程（F-QCLE）的方法。第一种方法将标准QCLE的操作员形式投射到绝热的浮雕基础上，然后转换为绝热表示形式。第二种方法将QCLE直接投射到浮雕的绝热基础上。两种方法产生的形式与通常的QCLE相似，具有两个修改：1。电子自由度扩展到无限的尺寸。 2。核运动遵循浮部准能量表面。但是，第二种方法包括额外的跨导数力，这是由于对浮雕绝热状态的时间和核运动的双重依赖性。我们的分析和数值测试表明，这种交叉衍生力是一种人造工具，这表明人们无法安全地将浮球状态投影的顺序与绝热转化交换。我们的结果与Izmaylov等人的类似发现一致，他们发现转换为绝热表示形式必须始终是应用的最后一个操作，尽管现在我们将这一结果扩展到了时间依赖的哈密顿量。本文和F-Qcle的适当推导应为进一步改善浮光表面跳跃的基础。
We investigate two approaches to derive the proper Floquet-based quantum-classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis, then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form which is similar to the usual QCLE with two modifications: 1. The electronic degrees of freedom are expanded to infinite dimension. 2. The nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a factitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., who found that transforming to the adiabatic representation must always be the last operation applied, though now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.
