**MAURO FABRIZIO**

*
An envolution model for the Ginzburg-Landau equations
*

**Pages** 155-169

**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.

Home Riv.Mat.Univ.Parma