Quantum-classical path integral. I. Classical memory and weak quantum nonlocality
Quantum-classical path integral. I. Classical memory and weak quantum nonlocality
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DOI：
10.1063/1.4767931
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发表时间：
2012-12-14
影响因子：
4.4
通讯作者：
Makri, Nancy
中科院分区：
文献类型：
--
作者：
Lambert, Roberto;Makri, Nancy
我们考虑耦合到多原子环境的量子系统动力学的严格路径积分描述，假设后者很好地近似于经典轨迹。早期的工作已经导出了来自环境的影响函数的半经典或纯经典表达式，对于许多情况应该足够准确，但是量子-（半）经典路径积分（QCPI）表达式的评估对于大规模模拟并不实用，因为与环境的相互作用在时间上引入了非局部耦合。在这项工作中，我们根据观测结果分析了环境对系统的影响的性质[N。Makri， J. Chem。路径积分的真正非定域性是一种严格的量子力学现象。物理学报，109,2994（1998）。如果环境是经典的，路径积分变成局部的，并且可以沿着自由溶剂的经典轨迹以逐步的方式进行评估。这个简单的QCPI“经典路径”限制通过经典机制完全捕获了系统的退相干。通过一种廉价的随机跳跃QCPI模型，可以获得对经典路径QCPI近似的小修正，该模型可以解释一些“反反应”效应。利用非定域性的有限长度，我们认为通过路径积分的迭代计算进一步包含量子退相干是可能的。最后，我们证明了量子振幅因子相对于系统路径的总和导致作为轨迹初始条件的函数的光滑被积，允许使用蒙特卡罗方法进行多维相空间积分。(C) 2012年美国物理研究所。[http://dx.doi.org/10.1063/1.4767931]
We consider rigorous path integral descriptions of the dynamics of a quantum system coupled to a polyatomic environment, assuming that the latter is well approximated by classical trajectories. Earlier work has derived semiclassical or purely classical expressions for the influence functional from the environment, which should be sufficiently accurate for many situations, but the evaluation of quantum-(semi)classical path integral (QCPI) expressions has not been practical for large-scale simulation because the interaction with the environment introduces couplings nonlocal in time. In this work, we analyze the nature of the effects on a system from its environment in light of the observation [N. Makri, J. Chem. Phys. 109, 2994 (1998)] that true nonlocality in the path integral is a strictly quantum mechanical phenomenon. If the environment is classical, the path integral becomes local and can be evaluated in a stepwise fashion along classical trajectories of the free solvent. This simple "classical path" limit of QCPI captures fully the decoherence of the system via a classical mechanism. Small corrections to the classical path QCPI approximation may be obtained via an inexpensive random hop QCPI model, which accounts for some "back reaction" effects. Exploiting the finite length of nonlocality, we argue that further inclusion of quantum decoherence is possible via an iterative evaluation of the path integral. Finally, we show that the sum of the quantum amplitude factors with respect to the system paths leads to a smooth integrand as a function of trajectory initial conditions, allowing the use of Monte Carlo methods for the multidimensional phase space integral. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767931]