Classical mechanics and the spreading of localized wave packets in condensed phase molecular systems
Classical mechanics and the spreading of localized wave packets in condensed phase molecular systems
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DOI：
10.1063/1.479449
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发表时间：
1999-08-01
影响因子：
4.4
通讯作者：
Coker, DF
中科院分区：
文献类型：
--
作者：
Herman, MF;Coker, DF
探讨了混沌多体系统中经典轨线的发散、量子波包的扩展以及经典分子动力学的有效性和应用之间的关系。这种分析，这是基于半经典描述的波函数传播的加权积分在一个旅行固定宽度的相干态的基础上，表明在混沌多体系统中的附近的经典轨迹的指数发散，应导致快速离域的初始本地化的量子波包描述系统的状态。因此，对这些所谓的经典系统使用经典分子动力学方法的理由不能基于系统波函数保持局部化的图像，因为它的中心遵循近似经典的轨迹。另一方面，系统密度的量子演化需要两个传播子，每个传播子在半经典图像中表示为轨迹上的积分。从这两个集成在经典的轨迹的贡献之间的干扰集中在这个轨迹对空间，这是发生在对中的两个轨迹是相同的最重要的点上的分析。对经典分子动力学所描述的系统的初始密度作了合理的假设，并对半经典描述中所采用的相干态基的宽度作了适当的选择，结果表明，含时观测量和关联函数的半经典表达式使纯经典表达式简化，尽管初始定域的波包对于相同的系统将快速地离域。(C)1999年美国物理学会。[S0021-9606（99）00229-9]。
The relationship between the diverging of classical trajectories in chaotic many-body systems, the spreading of quantum wave packets, and the validity and use of classical molecular dynamics is explored. This analysis, which is based on the semiclassical description of wave function propagation in terms of a weighted integration over a traveling fixed width coherent state basis, suggests that the exponential divergence of nearby classical trajectories in chaotic many-body systems should result in the rapid delocalization of an initially localized quantum wave packet describing the state of the system. Thus the justification for the use of classical molecular dynamics procedures for these supposedly classical systems cannot be based on the picture of the system wave function remaining localized as its center follows a nearly classical trajectory. The quantum evolution of the system density, on the other hand, requires two propagators, and each of these propagators is represented as an integration over trajectories in the semiclassical picture. The interference between the contributions from these two integrations over classical trajectories focuses the analysis on the most important points in this trajectory pair space, which are shown to occur when both trajectories in the pair are the same. Given reasonable assumptions for the initial density for a system that is expected to be well described by classical molecular dynamics, and given an appropriate choice for the width of the coherent state basis which is employed in the semiclassical description, it is shown that the semiclassical expressions for time dependent observables and correlation functions reduce the purely classical expressions, despite the fact that an initially localized wave packet would rapidly delocalize for the same system. (C) 1999 American Institute of Physics. [S0021-9606(99)00229-9].