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[1]何 健.运用变分法计算Ginzburg-Landau能量时的“涡旋”模型[J].绵阳师范学院学报,2018,(02):33-39.[doi:10.16276/j.cnki.cn51-1670/g.2018.02.007]
 HE Jian.The "Vortex" Model for Calculating Ginzburg-Landau Energy by Variational Method[J].Journal of Mianyang Normal University,2018,(02):33-39.[doi:10.16276/j.cnki.cn51-1670/g.2018.02.007]
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运用变分法计算Ginzburg-Landau能量时的“涡旋”模型(PDF)
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《绵阳师范学院学报》[ISSN:1672-612X/CN:51-1670/G]

卷:
期数:
2018年02期
页码:
33-39
栏目:
物理与电子信息技术
出版日期:
2018-02-25

文章信息/Info

Title:
The "Vortex" Model for Calculating Ginzburg-Landau Energy by Variational Method
文章编号:
1672-612X(2018)02-0033-07
作者:
何 健
绵阳师范学院数理学院,四川绵阳 621006
Author(s):
HE Jian
School of Mathematics and Physics,Mianyang Teachers' College,Mianyang, Sichuan 621006
关键词:
金斯堡-朗道能量 涡旋 流密度 调和方程 能量泛函
Keywords:
Ginzburg-Landau energy vortex current density harmonic equation energy functional
分类号:
O469
DOI:
10.16276/j.cnki.cn51-1670/g.2018.02.007
文献标志码:
A
摘要:
为给出Ginzburg-Landau能量的变分集合,本文讨论了一简化办法:以“涡旋”的增减对应的能量表述来实现集合的构建.为此,文章首先对Ginzburg-Landau能量的泛函性质给予了说明,然后针对相变区域,提出“涡旋”模型并进行了数学描述,最后详细计算了涡旋自能、互能及总能.在分析过程中所做的一些模型的构建、数学技巧的使用及辅助办法的引入对于处理“涡旋”类拓扑缺陷都有重要意义,具有一定示范作用.
Abstract:
To give Ginzburg-Landau energy variational collection, this paper discusses a simplified way: through the "vortex" corresponding to increase or decrease of the objects of this energy, the collection building can be realized. This paper first illustrates the nature of the Ginzburg-Landau energy is a kind of functional, then in view of the phase transition area, puts forward "the vortex" model and the mathematical description, with detailed calculations of vortex own energy, interaction energy and the total energy. In analyzing some model building, mathematical skills and auxiliary measures for handling the "vortex" kind of topological defects are employed, which is beneficial and referential for the study in this field.

参考文献/References:

[1] Tinkham M.Introduction to Superconductivity[M].2nd edn.McGraw-Hill,New York:Dover Publications,2004-6-14.
[2] DeGennes P G.Superconductivity of Metal and Alloys[M].New York:Benjamin,1966.
[3] Bethuel F,Brezis H,Hélein F.Ginzburg-Landau Vortices[M]. Boston:Birkhäuser,1994.
[4] Jeerard R L,Soner C.The Jacobian and the Ginzburg-Landau energy[J]. Caculus of Variations and Partial Differential Equations,2002,14(2):151-191.
[5] Sandier E, Serfaty S.Vortices in the Magnetic Ginzburg-Landau Model[M].Boston:Birkhäuser,2007.
[6] Lawrence W E,Doniach S.Development of low temperature physics.Present situation Proceedings of the Twelfth International Conference on Low Temperature Physics[C].Kyoto,Japan:Kanda,1970.
[7] 黄昆,韩汝琦.固体物理学[M].北京:高等教育出版社,1988,10:481-484.
[8] 四川大学数学系高等数学、微分方程教研室.数学物理方法:第4册[M].北京:高等教育出版社,1985,6:236-240.

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备注/Memo

备注/Memo:
收稿日期:2017-11-01
作者简介:何健(1980— ),男,四川自贡人,讲师,硕士,研究方向:理论物理、光学.
更新日期/Last Update: 2018-02-25