Park Kisam, Poirier Bill, Parlant Gérard
Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA.
J Chem Phys. 2008 Nov 21;129(19):194112. doi: 10.1063/1.3013630.
Quantum trajectory methods (QTMs) hold great promise as a potential means of obtaining dynamical insight and computational scaling similar to classical trajectory simulations but in an exact quantum dynamical context. To date, the development of QTMs has been stymied by the "node problem"--highly nonclassical and numerically unstable trajectories that arise when the wavepacket density |psi|2 exhibits substantial interference oscillations. In a recent paper, however [B. Poirier, J. Chem. Phys. 128, 164115 (2008)], a "bipolar decomposition," psi=psi+(+)(psi)psi(-), was introduced for one-dimensional (1D) wavepacket dynamics calculations such that the component densities |psi(+)(-)|2 are slowly varying and otherwise interference-free, even when |psi|2 itself is highly oscillatory. The bipolar approach is thus ideally suited to a QTM implementation, as is demonstrated explicitly in this paper. Two model 1D benchmark systems exhibiting substantial interference are considered--one with more "quantum" system parameters and the other more classical-like. For the latter, more challenging application, synthetic QTM results are obtained and found to be extremely accurate, as compared to a corresponding fixed-grid calculation. Ramifications of the bipolar QTM approach for the classical limit and also for multidimensional applications, are discussed.
量子轨迹方法（QTMs）有望成为一种潜在手段，以获取类似于经典轨迹模拟的动力学见解和计算规模，但却是在精确的量子动力学背景下。迄今为止，QTMs的发展一直受到“节点问题”的阻碍——当波包密度|ψ|²表现出大量干涉振荡时出现的高度非经典且数值不稳定的轨迹。然而，在最近的一篇论文中[B. 波里尔，《化学物理杂志》128, 164115 (2008)]，针对一维（1D）波包动力学计算引入了一种“双极分解”，即ψ = ψ⁺(+)ψψ⁻，使得分量密度|ψ(+)( -)|²缓慢变化且无其他干涉，即使|ψ|²本身高度振荡。本文明确证明，双极方法因此非常适合QTM实现。考虑了两个表现出大量干涉的一维基准模型系统——一个具有更多“量子”系统参数，另一个更具经典特征。对于后一种更具挑战性的应用，与相应的固定网格计算相比，获得了合成QTM结果并发现其极其准确。讨论了双极QTM方法对于经典极限以及多维应用的影响。
