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Updated: Apr 12, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
Timothy J H Hele1, Michael J Willatt1, Andrea Muolo1
1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Abstract:
We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the "Classical Wigner" approximation. Here, we show that the further approximation of this "Matsubara dynamics" gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. These findings are consistent with previous numerical results and give explicit formulae for the terms that CMD and RPMD leave out.
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