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Mass-Zero constrained dynamics and statistics for the shell model in magnetic field

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  • D. D. Girardier

    (Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne)

  • A. Coretti

    (Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne
    Department of Mathematical Sciences, Politecnico di Torino)

  • G. Ciccotti

    (Institute for Applied Computing “Mauro Picone” (IAC)
    Università di Roma La Sapienza
    School of Physics, University College of Dublin UCD-Belfield)

  • S. Bonella

    (Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne)

Abstract

In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics of physical degrees of freedom. In this paper, we discuss a recent algorithm proposed to efficiently and rigorously simulate this type of systems: the Mass-Zero (MaZe) Constrained Dynamics. In MaZe, the minimum condition is imposed as a constraint on the auxiliary variables treated as degrees of freedom of zero inertia driven by the physical system. The method is formulated in the Lagrangian framework, enabling the properties of the approach to emerge naturally from a fully consistent dynamical and statistical viewpoint. We begin by presenting MaZe for typical minimization problems where the imposed constraints are holonomic and summarizing its key formal properties, notably the exact Born–Oppenheimer dynamics followed by the physical variables and the exact sampling of the corresponding physical probability density. We then generalize the approach to the case of conditions on the auxiliary variables that linearly involve their velocities. Such conditions occur, for example, when describing systems in external magnetic field and they require to adapt MaZe to integrate semiholonomic constraints. The new development is presented in the second part of this paper and illustrated via a proof-of-principle calculation of the charge transport properties of a simple classical polarizable model of NaCl.

Suggested Citation

  • D. D. Girardier & A. Coretti & G. Ciccotti & S. Bonella, 2021. "Mass-Zero constrained dynamics and statistics for the shell model in magnetic field," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-20, August.
  • Handle: RePEc:spr:eurphb:v:94:y:2021:i:8:d:10.1140_epjb_s10051-021-00165-0
    DOI: 10.1140/epjb/s10051-021-00165-0
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    References listed on IDEAS

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    1. M. Armand & J.-M. Tarascon, 2008. "Building better batteries," Nature, Nature, vol. 451(7179), pages 652-657, February.
    2. Xiufeng Tang & Guoxin Chen & Zhaopeng Mo & Dingbang Ma & Siyuan Wang & Jinxiu Wen & Li Gong & Lite Zhao & Jingcheng Huang & Tengcheng Huang & Jianyi Luo, 2019. "Controllable two-dimensional movement and redistribution of lithium ions in metal oxides," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
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