Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics

• Published in: The Journal of chemical physics Vol. 142; no. 19; p. 191101
• Main Authors: Hele, Timothy J. H., Willatt, Michael J., Muolo, Andrea, Althorpe, Stuart C.
• Format: Journal Article
• Language: English
• Published: United States 21.05.2015
• Subjects: APPROXIMATIONS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; FLUCTUATIONS; MEAN-FIELD THEORY; MOLECULAR DYNAMICS METHOD; POLYMERS; QUANTUM MECHANICS
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.4921234

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.