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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:423

Article

Lu, Jianfeng^1,2  Lu, Yulong³  Zhou, Zhennan⁴ 

[1] Duke Univ, Dept Math, Dept Phys, Durham, NC 27708 USA

[2] Duke Univ, Dept Chem, Durham, NC 27708 USA

[3] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[4] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

关键词: Preconditioned Langevin dynamics;    Path integral molecular dynamics;    Continuum limit;    Dimension-independent convergence rate;   

DOI  :  10.1016/j.jcp.2020.109788

来源: Elsevier

【 摘 要 】

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 present a careful mode analysis of the preconditioned dynamics and show their connections to the normal mode, the staging coordinate and the Matsubara mode representation for ring polymers. In the case where the potential is quadratic, we show that the continuum limit of the preconditioned mass modified Langevin dynamics converges to its equilibrium exponentially fast, which suggests that the finite dimensional counterpart has a dimension-independent convergence rate. 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free