Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA.
J Chem Phys. 2023 May 14;158(18). doi: 10.1063/5.0146654.
We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.
我们引入了一种基于马瑟巴哈动力学的半经典近似方法，用于计算广义多时间相关函数，这是一种保持量子玻尔兹曼分布的经典动力学方法。该方法在零时间和调和极限下是精确的，并且当仅考虑一个马瑟巴哈模式（即质心）时简化为经典动力学。广义多时间相关函数可以表示为正则相空间积分，涉及通过平滑马瑟巴哈空间中的泊松括号耦合的经典演化可观测量。在简单势上的数值测试表明，马瑟巴哈近似法与精确结果的一致性优于经典动力学，为多时间相关函数的纯量子和经典描述之间提供了一座桥梁。尽管相位问题阻止了马瑟巴哈动力学的实际应用，但所报道的工作为未来发展用于凝聚相系统化学动力学研究的保持量子玻尔兹曼分布的半经典近似方法提供了一个基准理论。
