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On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods

Jingrun Chen Soochow University Jian-Guo Liu Duke University Zhennan Zhou Duke University

Analysis of PDEs mathscidoc:1702.03021

Multiscale Modeling and Simulation, 14, (4), 1463-1487, 2016.2
From a variational perspective, we derive a series of magnetization and quantum spin current systems coupled via an “s-d” potential term, including the Schrödinger--Landau--Lifshitz--Maxwell system, the Pauli--Landau--Lifshitz system, and the Schrödinger--Landau--Lifshitz system with successive simplifications. For the latter two systems, we propose using the time splitting spectral method for the quantum spin current and the Gauss--Seidel projection method for the magnetization. Accuracy of the time splitting spectral method applied to the Pauli equation is analyzed and verified by numerous examples. Moreover, behaviors of the Schrödinger--Landau--Lifshitz system in different “s-d” coupling regimes are explored numerically.
Landau--Lifshitz equation, Schrödinger equation, Pauli equation, time splitting spectral method, variational structure
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@inproceedings{jingrun2016on,
  title={On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods},
  author={Jingrun Chen, Jian-Guo Liu, and Zhennan Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207210836174700263},
  booktitle={Multiscale Modeling and Simulation},
  volume={14},
  number={4},
  pages={1463-1487},
  year={2016},
}
Jingrun Chen, Jian-Guo Liu, and Zhennan Zhou. On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods. 2016. Vol. 14. In Multiscale Modeling and Simulation. pp.1463-1487. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207210836174700263.
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