Ginzburg–Landau equation

Summary

The Ginzburg–Landau equations describe a superconductor through a complex order parameter $\psi$ and a magnetic vector potential $A$. They are the Euler–Lagrange equations of the Ginzburg–Landau energy, which penalises variations of $\psi$, deviations of $\abs{\psi}$ from $1$, and magnetic energy. The quantity $\abs{\psi}^2$ measures the density of superconducting electrons. Their solutions include vortices, points or lines around which $\psi$ winds and where $\abs{\psi}$ vanishes.