Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

DOI10.1017/S0956792500001558zbMath0817.35112MaRDI QIDQ4764823

Charles M. Elliott, Tang Qi, Hiroshi Matano

Publication date: 7 August 1995

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

energy functionalgauge invarianceGibbs free energycomplex Ginzburg- Landau order parameter

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Statistical mechanics of superconductors (82D55) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

Remark on a relation between magnetic field and topological degree of order parameter in a type-II superconductivity model ⋮ Stability and convergence of Strang splitting. II: Tensorial Allen-Cahn equations ⋮ Long time behavior of the Ginzburg-Landau superconductivity equations ⋮ Time dependent Ginzburg-Landau equations of superconductivity ⋮ Nodal sets of solutions of equations involving magnetic Schrödinger operator in three dimensions ⋮ On the minimizers of the Ginzburg-Landau energy for high kappa: The axially symmetric case ⋮ Hausdorff measure of critical sets of solutions to magnetic Schrödinger equations ⋮ Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model ⋮ \(\Gamma\)-convergence and the emergence of vortices for Ginzburg-Landau on thin shells and manifolds ⋮ Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold ⋮ Existence of periodic solutions for Ginzburg-Landau equations of superconductivity ⋮ On the Betti numbers of level sets of solutions to elliptic equations

Cites Work

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• Vortices in complex scalar fields
• The effect of a singular perturbation on nonconvex variational problems
• Symmetry and related properties via the maximum principle
• A boundary value problem related to the Ginzburg-Landau model
• The gradient theory of phase transitions and the minimal interface criterion
• Symmetric vortices for the Ginzberg-Landau equations of superconductivity and the nonlinear desingularization phenomenon
• Normal/superconducting transitions in Landau–Ginzburg theory
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Macroscopic Models for Superconductivity

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