Multi-time Formulation of Matsubara Dynamics

TL;DR

This paper extends Matsubara dynamics to multi-time correlation functions, providing a theoretical benchmark for future semi-classical approximations in quantum dynamics.

Contribution

It generalizes Matsubara dynamics to evaluate multi-time correlation functions, establishing a benchmark theory for higher order quantum correlation calculations.

Findings

Proposes a multi-time Matsubara dynamics approximation.

Shows the approximation can evaluate symmetrized double Kubo functions.

Provides a theoretical foundation for future semi-classical methods.

Abstract

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 multi-time correlation functions. We 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 multi-time realm, a multi-time Matsubara dynamics approximation can be obtained for the multi-time fully symmetrized Kubo transformed correlation function. Although not a practical method, due to the presence of a phase-term, this multi-time formulation of Matsubara dynamics represents a benchmark theory for future development of Boltzmann preserving semi-classical approximations to general higher order multi-time correlation functions.