Matsubara trajectory study of centroid molecular dynamics

Matsubara dynamics, first proposed in 2015, is a theory that combines classical dynamics with quantum statistics. It has helped to explain the theoretical basis for other quantum molecular dynamics methods including centroid molecular dynamics (CMD). It has been observed that for the one-dimensional q-TIP4P/F potential under the Feynman-Kleinert approximation, CMD and Matsubara trajectories follow each other at short times. In this work we show that there is a systematic clustering of Matsubara trajectories around the CMD trajectory, given a correct sampling of the non-centroid modes. We were also able to conclude that this is not due to weak coupling of the non-centroid modes with the centroid. Post-averaging of Matsubara trajectories gives a good agreement with CMD, which suggests that an expansion of the fluctuation force around the centroid force may help to explain CMD.