A new method for wave packet dynamics: Derivative propagation along quantum trajectories
A new method for wave packet dynamics: Derivative propagation along quantum trajectories
复制标题
波包动力学的新方法：沿量子轨迹的导数传播
DOI：
10.1063/1.1578061
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发表时间：
2003
影响因子：
4.4
通讯作者：
R. Wyatt
中科院分区：
文献类型：
--
作者：
C. Trahan;K. Hughes;R. Wyatt
提出了一种计算量子力学波包时间演化的新方法。在复杂作用S=C(r,t)+iS(r,t)/ h, ψ(r,t)=exp(S)下，实值函数C和S的运动方程涉及到C和S的梯度和曲率。在以前的流体力学公式实现中，使用了各种耗时且精度有限的拟合技术来计算演化系综中每个流体单元周围的导数。在本研究中，为空间导数本身建立了运动方程，其中一小部分沿着量子轨迹与C和s的方程同时积分。值得注意的是，量子效应可以包括在各种近似阶，不涉及空间拟合，不存在基集展开，单个量子轨迹（而不是相关的系综）可以一次传播一个。将导数传播法应用于非调和p方程，得到了很好的结果。
A new method is proposed for computing the time evolution of quantum mechanical wave packets. Equations of motion for the real-valued functions C and S in the complex action S=C(r,t)+iS(r,t)/ℏ, with ψ(r,t)=exp(S), involve gradients and curvatures of C and S. In previous implementations of the hydrodynamic formulation, various time-consuming fitting techniques of limited accuracy were used to evaluate these derivatives around each fluid element in an evolving ensemble. In this study, equations of motion are developed for the spatial derivatives themselves and a small set of these are integrated along quantum trajectories concurrently with the equations for C and S. Significantly, quantum effects can be included at various orders of approximation, no spatial fitting is involved, there are no basis set expansions, and single quantum trajectories (rather than correlated ensembles) may be propagated, one at a time. Excellent results are obtained when the derivative propagation method is applied to anharmonic p...