Abstract
The minimization of the Ginzburg-Landau (GL) free energy with respect to two independent variables, the vector potential and complex order parameter leads to two independent equations, the GL equations. The equation given by the variation of the vector potential yields an equation similar to the London equation, whereas variation of the order parameter yields anequation describing the spatial dependence of the order parameter, which indicates that the number of superelectrons is not constant but depends on position, which is a feature not included in the London theory. The two GL equations yield two characteristic lengths, the penetration depth of the magnetic field similar in form to the London penetration depth and temperature-dependent GL coherence length, which characterizes the spatial variation of the order parameter.
