Real time quantum dynamics preaveraged over imaginary time path integral: A formal basis for both Centroid Molecular Dynamics and Ring Polymer Molecular Dynamics

TL;DR

This paper develops a rigorous theoretical framework for real-time quantum dynamics based on imaginary time path integrals, unifying and extending centroid and ring polymer molecular dynamics methods for condensed phase systems.

Contribution

It provides a formal basis connecting centroid and ring polymer molecular dynamics, enabling analysis and development of new quantum dynamics methods.

Findings

Unifies centroid and ring polymer dynamics under a rigorous formalism

Clarifies the theoretical foundations of existing quantum dynamics approximations

Suggests potential for new quantum dynamics methods using cyclic imaginary time paths

Abstract

An exact real time quantum dynamics preaveraged over imaginary time path integral is formulated for general condensed phase equilibrium ensemble. This formulation results in the well-known centroid dynamics approach upon filtering of centroid constraint, and provides a rigorous framework to understand and analyze a related quantum dynamics approximation method called ring polymer molecular dynamics. The formulation also serves as the basis for developing new kinds of quantum dynamics that utilize the cyclic nature of the imaginary time path integral.