Jung Kenneth A, Videla Pablo E, Batista Victor S
Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA.
J Chem Phys. 2019 Jul 21;151(3):034108. doi: 10.1063/1.5110427.
Matsubara dynamics has recently emerged as the most general form of a quantum-Boltzmann-conserving classical dynamics theory for the calculation of single-time correlation functions. Here, we present a generalization of Matsubara dynamics for the evaluation of multitime correlation functions. We first show that the Matsubara approximation can also be used to approximate the two-time symmetrized double Kubo transformed correlation function. By a straightforward extension of these ideas to the multitime realm, a multitime Matsubara dynamics approximation can be obtained for the multitime fully symmetrized Kubo transformed correlation function. Although not a practical method, due to the presence of a phase-term, this multitime formulation of Matsubara dynamics represents a benchmark theory for future development of Boltzmann preserving semiclassical approximations to general higher order multitime correlation functions. It also reveals a connection between imaginary time-ordering in the path integral and the classical dynamics of multitime correlation functions.
松原动力学最近已成为用于计算单时关联函数的量子玻尔兹曼守恒经典动力学理论的最一般形式。在此，我们提出一种松原动力学的推广形式，用于评估多时关联函数。我们首先表明，松原近似也可用于近似双时对称化双久保变换关联函数。通过将这些思想直接扩展到多时领域，可得到多时完全对称化久保变换关联函数的多时松原动力学近似。尽管由于存在相位项而不是一种实用方法，但这种多时松原动力学表述代表了未来玻尔兹曼守恒半经典近似到一般高阶多时关联函数发展的基准理论。它还揭示了路径积分中的虚时排序与多时关联函数的经典动力学之间的联系。
