Multi-time Formulation of Matsubara Dynamics

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.

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• Non-adiabatic Ring Polymer Molecular Dynamics in the Phase Space of the SU(N) Lie Group
• Open quantum systems beyond equilibrium: Lindblad equation and path integral molecular dynamics
• Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy