Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801, USA.
J Chem Phys. 2012 Dec 14;137(22):22A552. doi: 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.
我们考虑了量子系统与多原子环境耦合的动力学的严格路径积分描述，假设后者可以通过经典轨迹很好地近似。早期的工作已经从环境中推导出了影响泛函的半经典或纯经典表达式，这对于许多情况来说应该足够准确，但由于与环境的相互作用在时间上引入了非局部耦合，因此对量子-（半）经典路径积分（QCPI）表达式的评估在大规模模拟中并不实用。在这项工作中，我们根据观察结果分析了系统与其环境之间相互作用的性质，即路径积分中的真正非局域性是一种严格的量子力学现象。如果环境是经典的，路径积分就会变得局部化，可以沿着自由溶剂的经典轨迹逐步进行评估。这种简单的 QCPI“经典路径”极限通过经典机制完全捕捉到了系统的退相干。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“反向反应”效应。利用非局域性的有限长度，我们认为可以通过对路径积分的迭代评估来进一步包含量子退相干。最后，我们表明，关于系统路径的量子幅度因子的和导致了轨迹初始条件的函数的平滑积分核，从而允许使用蒙特卡罗方法进行多维相空间积分。
