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  "body": "\n## Summary\n\nThe Ginzburg–Landau equations describe a superconductor through a complex order parameter $\\psi$ and a magnetic vector potential $A$.\nThey are the Euler–Lagrange equations of the Ginzburg–Landau energy, which penalises variations of $\\psi$, deviations of $\\abs{\\psi}$ from $1$, and magnetic energy.\nThe quantity $\\abs{\\psi}^2$ measures the density of superconducting electrons.\nTheir solutions include vortices, points or lines around which $\\psi$ winds and where $\\abs{\\psi}$ vanishes.\n\n## Explanations\n\n### L1 human\n\nBelow a critical temperature some metals conduct electricity with no resistance and push out magnetic fields.\nGinzburg and Landau described this state by a complex number $\\psi$ at each point.\nWhere $\\abs{\\psi}$ is near $1$ the metal is superconducting, and where it is $0$ the metal is normal.\nThe energy prefers $\\abs{\\psi} = 1$, prefers $\\psi$ to vary slowly, and charges for magnetic field.\nThe two simplest solutions are the fully superconducting state $\\psi = 1$ with no field and the normal state $\\psi = 0$ with a uniform field.\nIn between, a magnetic field can enter through thin vortex tubes.\n",
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