An envolution model for the Ginzburg-Landau equations
Received: 3 October 1999
Mathematics Subject Classification (2000): 82D55 - 81J05
Abstract The aim of this paper is addressed to the study of the Ginzburg-Landau theory that yields the behaviour of a superconductor near to the transition phase. We show that the pertinent equations can be derived starting from the representation of the free energy in terms of the magnetic field H , instead of the vector potential A, such that Ñ ´ A =m H, and the modulus |y|, which denotes the concentration of superconducting electrons, instead of the complex parameter y. Such a representation gives also a conceptual simplification of the model since it makes use of observable quantities. In addition, the free energy in terms of H and |y| makes the theory gauge-invariant in that is free from the vector potential A and the phase of y. The compatibility with thermodynamics is examined and it follows that the generality of the second law is related to the specific approximation of the model.