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Regular and Chaotic Dynamics, 2021, Volume 26, Issue 2, Pages 183–204
DOI: https://doi.org/10.1134/S1560354721020064 (Mi rcd1110) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Special Issue: Nonlinear Dynamics in Chemical Sciences: Part II

On Ergodicity for Multidimensional Harmonic Oscillator Systems with Nosé – Hoover-type Thermostat

Ikuo Fukudaab, Kei Moritsuguc, Yoshifumi Fukunishid

a Institute for Protein Research, Osaka University, 565-0871 Osaka, Japan
b Graduate School of Simulation Studies, University of Hyogo, 650-0047 Kobe, Japan
c Graduate School of Medical Life Science, Yokohama City University, 230-0045 Yokohama, Japan
d Cellular and Molecular Biotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 135-0064 Tokyo, Japan
Citations (1)
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DOI: https://doi.org/10.1134/S1560354721020064
Abstract: A simple proof and a detailed analysis of the nonergodicity for multidimensional harmonic oscillator systems with the Nosé – Hoover-type thermostat are presented. The origin of the nonergodicity is the symmetries in the multidimensional target physical system, and it differs from that in the Nosé – Hoover thermostat with the one-dimensional harmonic oscillator. A new and simple deterministic method to recover the ergodicity is also proposed. An individual thermostat variable is attached to each degree of freedom, and all of these variables act on a friction coefficient for each degree of freedom. This action is linear and controlled by a Nosé mass matrix $\mathbf{Q}$, which is the matrix analogue of the scalar Nosé mass. The matrix $\mathbf{Q}$ can break the symmetry and contribute to the ergodicity.
Keywords: ergodicity, Nosé – Hoover equation, thermostat, molecular dynamics, invariant space, multidimensional harmonic oscillator, Nosé-mass matrix, density dynamics.
Funding agency Grant number
Japan Society for the Promotion of Science 17K05143
20K11854
This work was supported by a Grant-in-Aid for Scientific Research (C) (17K05143 and 20K11854) from JSPS and the “Development of innovative drug discovery technologies for middlesized molecules” from the Japan Agency for Medical Research and Development, AMED.
Received: 17.08.2020
Accepted: 13.03.2021
Bibliographic databases:
Document Type: Article
MSC: 34A34, 37A10, 70F40, 82B80
Language: English
Citation: Ikuo Fukuda, Kei Moritsugu, Yoshifumi Fukunishi, “On Ergodicity for Multidimensional Harmonic Oscillator Systems with Nosé – Hoover-type Thermostat”, Regul. Chaotic Dyn., 26:2 (2021), 183–204
Citation in format AMSBIB
\Bibitem{FukMorFuk21}
\by Ikuo Fukuda, Kei Moritsugu, Yoshifumi Fukunishi
\paper On Ergodicity for Multidimensional Harmonic Oscillator
Systems with Nosé – Hoover-type Thermostat
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 2
\pages 183--204
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  • https://www.mathnet.ru/eng/rcd1110
  • https://www.mathnet.ru/eng/rcd/v26/i2/p183
    • This publication is cited in the following 1 articles:
    1. Ikuo Fukuda, Kei Moritsugu, “Analyses of the perturbative motion in the coupled Nosé–Hoover equation for assessing the system parameter values”, J. Phys. A: Math. Theor., 58:13 (2025), 135001  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:126
    References:27
     
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