Gauge invariance and time-dependence Ginzburg-Landau equations (Q2756119)

The paper works within the London theory of superconductivity, which contains only the first London equation for superconducting current \({\mathbf J}_s\) at constant temperatures below the critical value \(T_c\). The free energy of the Ginzburg-Landau theory is considered within this modified London theory. It is shown that a pair of equations, which are equivalent to the usual Ginzburg-Landau equations, may be derived. These alternative equations and the free energy involve only the modulus \(|\psi|\) of the complex order parameter \(\psi\) and the magnetic field \({\mathbf H}\), whereas usually they are written as a function of \(\psi\) and the vector potential \({\mathbf A}\). Consequently, the theory must automatically be gauge-invariant. NEWLINENEWLINENEWLINEThe Ginzburg-Landau equations have been developed for an evolution model by Gor'kov and Èliashberg, starting from microscopic B.C.S. model. In such extension the term \({{\partial {\mathbf E}}\over{\partial t}}\) of the first Maxwell equation is assumed to be negligeable. Therefore, this new system represents an approximated problem, which is called quasi-dynamic model. Moreover, it is possible to prove the compatibility of this new model with the thermodynamic laws.