Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics

Journal Article

We investigate the continuum limit that the number of beads goes to infinity in the ring polymer representation of thermal averages. Studying the continuum limit of the trajectory sampling equation sheds light on possible preconditioning techniques for sampling ring polymer configurations with large number of beads. We propose two preconditioned Langevin sampling dynamics, which are shown to have improved stability and sampling accuracy. We also present analysis of the preconditioned Langevin dynamics and their connections to the normal mode, the staging coordinate and the Matsubara mode representation for ring polymers. In addition, the preconditioning techniques can be naturally applied to the multi-level quantum systems in the nonadiabatic regime, which are compatible with various numerical approaches.

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Duke Authors

Cited Authors

  • Lu, J; Zhou, Z