Physical Presentation of the Model—Critical Fields

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 70)


We begin by describing how the expression (1.1) for the Ginzburg-Landau functional is deduced from the expression (2.1) below, more commonly found in the physics literature. We will also give a nonrigorous introduction to critical fields in ℝ2, in the spirit of Abrikosov, and draw a corresponding phase diagram in the (ε, hex) plane, i.e., qualitatively describe minimizers of the Ginzburg-Landau energy for different values of ε and hex, emphasizing the role of the vortices. Three areas of the parameter plane will be found: the normal, superconducting and mixed states, separated by what are usually called critical lines.


Gauge Transformation Critical Field Hexagonal Lattice Critical Line Normal Solution 
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© Birkhäuser Boston 2007

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