Singularity analysis of Ginzburg–Landau energy related to p-wave superconductivity

被引:0
|
作者
Yutian Lei
机构
[1] Nanjing Normal University,Institute of Mathematics, School of Mathematics Sciences
来源
Zeitschrift für angewandte Mathematik und Physik | 2013年 / 64卷
关键词
35Q56; 49J45; 49Q20; 82D55; Ginzburg–Landau free energy functional; p-wave superconductivity; Weighted energy estimate; Concentration compactness; Quantization effect;
D O I
暂无
中图分类号
学科分类号
摘要
The following Ginzburg–Landau energy in the absence of a magnetic field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\varepsilon(\psi) = \int\limits_G\left[\frac{1}{2}|\nabla\psi|^2 + \frac{1}{4\varepsilon^2}(1-|\psi|^2)^2\right]{\rm d}x$$\end{document}was well studied during recent twenty years. Here, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G \subset \mathbf{R}^2}$$\end{document} is a bounded smooth domain, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\psi}$$\end{document} is an order parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon >0 }$$\end{document} . In particular, several global properties including the weighted energy estimation, the concentration compactness properties and the quantization effect of the energy had been established. This paper is concerned with another Ginzburg–Landau type free energy associated with p-wave superconductivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\varepsilon (\psi, u; G) = \frac{1}{2} \int\limits_G(|\nabla \psi|^2 + |\nabla u|^2 - |\nabla|\psi||^2){\rm d}x + \frac{1}{4\varepsilon^2} \int\limits_G(1-|\psi|^2)^2{\rm d}x.$$\end{document}Here, u is also an order parameter. We will prove that those global properties still hold for this more complicated energy functional. Such global properties describe the locations of the regular and the singular domains, and also show the convergence relation between the Ginzburg–Landau minimizers and the harmonic maps.
引用
收藏
页码:1249 / 1266
页数:17
相关论文
共 50 条
  • [1] Singularity analysis of Ginzburg-Landau energy related to p-wave superconductivity
    Lei, Yutian
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2013, 64 (04): : 1249 - 1266
  • [2] A generalization of the Ginzburg-Landau theory to p-wave superconductors
    Di Grezia, E.
    Esposito, S.
    Salesi, G.
    MODERN PHYSICS LETTERS B, 2008, 22 (18): : 1709 - 1716
  • [3] Ginzburg-Landau equations for layered p-wave superconductors
    Zhu, JX
    Ting, CS
    Shen, JL
    Wang, ZD
    PHYSICAL REVIEW B, 1997, 56 (21): : 14093 - 14101
  • [4] Singularity analysis of a p-Ginzburg-Landau type minimizer
    Lei, Yutian
    BULLETIN DES SCIENCES MATHEMATIQUES, 2010, 134 (01): : 97 - 115
  • [5] Derivation of the Ginzburg-Landau equations for a ferromagnetic p-wave superconductor
    Dahl, E. K.
    Sudbo, A.
    PHYSICAL REVIEW B, 2007, 75 (14):
  • [6] p-wave superconductivity
    Mackenzie, AP
    Maeno, Y
    PHYSICA B, 2000, 280 (1-4): : 148 - 153
  • [7] Aspects of p-wave superconductivity
    Maki, K
    Puchkaryov, E
    Wang, GF
    Won, H
    CHINESE JOURNAL OF PHYSICS, 2000, 38 (02) : 386 - 394
  • [8] Vortices in p-wave superconductivity
    Lin, FH
    Lin, TC
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 34 (05) : 1105 - 1127
  • [9] Quantization for a Ginzburg-Landau type energy related to superconductivity with normal impurity inclusion
    Lei, Yutian
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (01) : 243 - 259
  • [10] Vortex analysis in the Ginzburg-Landau model of superconductivity
    Sandier, E
    Serfaty, S
    NONLINEAR PDE'S IN CONDENSED MATTER AND REACTIVE FLOWS, 2002, 569 : 491 - 506