The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties

TLDR

The paper examines quantum dynamical time correlation functions using the path centroid variable in Feynman path integration, building on the centroid‑based equilibrium approach from the companion paper. The study introduces the centroid perspective into real‑time position correlation function calculations to explore a quasiclassical role for the centroid variable. The quasiclassical perspective is formulated for general interaction potentials, with computational effort scaling like classical molecular dynamics, and is implemented through several approaches to compute general time correlation functions. The theoretical results are illustrated and tested by representative numerical applications.

Abstract

The formulation of quantum dynamical time correlation functions is examined within the context of the path centroid variable in Feynman path integration. This study builds on the centroid-based approach to equilibrium properties developed in the companion paper. The introduction of the centroid perspective into the calculation of real time position correlation functions is outlined and an intriguing quasiclassical role for the centroid variable in real time position correlation functions is identified. This quasiclassical perspective is developed in terms of general interaction potentials, and the computational effort in implementing the method should scale with the size of the system in the same fashion as a classical molecular dynamics calculation. The centroid-based theory is also implemented in several different approaches to calculate general time correlation functions. The theoretical results are illustrated and tested by representative numerical applications.