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Title: Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics

Abstract

Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional density evolution, there exists another type of discrete evolution that may not correspond to a continuous, real dynamical counterpart. This virtual dynamics case is also able to produce the desired stationary distribution. Different types of repartition lead to different numerical schemes, of which the accuracy and efficiency are investigated through studying the harmonic oscillator potential, an analytical solvable model. By analyzing the asymptotic distribution and characteristic correlation time that are derived by either directly solving the discrete equations of motion or using the related phase space propagators, it is shown that the optimal friction coefficient resulting in the minimum characteristic correlation time depends on the time interval chosen in the numerical implementation. In conclusion, when the recommended “middle” scheme is employed, both analytical and numerical results demonstrate that, for good numerical performance in efficiency as well as accuracy, one may choose a friction coefficient in a wide range from around the optimal value to the high friction limit.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [2]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1];  [2]
  1. Peking University, Beijing (China). Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering
  2. Beijing Normal University, Beijing (China). College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1497877
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 18; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Li, Dezhang, Han, Xu, Chai, Yichen, Wang, Cong, Zhang, Zhijun, Chen, Zifei, Liu, Jian, and Shao, Jiushu. Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics. United States: N. p., 2017. Web. doi:10.1063/1.4996204.
Li, Dezhang, Han, Xu, Chai, Yichen, Wang, Cong, Zhang, Zhijun, Chen, Zifei, Liu, Jian, & Shao, Jiushu. Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics. United States. doi:10.1063/1.4996204.
Li, Dezhang, Han, Xu, Chai, Yichen, Wang, Cong, Zhang, Zhijun, Chen, Zifei, Liu, Jian, and Shao, Jiushu. Thu . "Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics". United States. doi:10.1063/1.4996204. https://www.osti.gov/servlets/purl/1497877.
@article{osti_1497877,
title = {Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics},
author = {Li, Dezhang and Han, Xu and Chai, Yichen and Wang, Cong and Zhang, Zhijun and Chen, Zifei and Liu, Jian and Shao, Jiushu},
abstractNote = {Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional density evolution, there exists another type of discrete evolution that may not correspond to a continuous, real dynamical counterpart. This virtual dynamics case is also able to produce the desired stationary distribution. Different types of repartition lead to different numerical schemes, of which the accuracy and efficiency are investigated through studying the harmonic oscillator potential, an analytical solvable model. By analyzing the asymptotic distribution and characteristic correlation time that are derived by either directly solving the discrete equations of motion or using the related phase space propagators, it is shown that the optimal friction coefficient resulting in the minimum characteristic correlation time depends on the time interval chosen in the numerical implementation. In conclusion, when the recommended “middle” scheme is employed, both analytical and numerical results demonstrate that, for good numerical performance in efficiency as well as accuracy, one may choose a friction coefficient in a wide range from around the optimal value to the high friction limit.},
doi = {10.1063/1.4996204},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 18,
volume = 147,
place = {United States},
year = {2017},
month = {11}
}

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