Abstract
The problem of the flux penetration of an infinite square plate of type I superconductor in a perpendicular magnetic field is analyzed perturbatively via the Ginzburg-Landau equations. It is shown that Landau's classic 1937 textbook model is at best a qualitative guide to the expected flux patterns. If the plate thickness d is near a critical scale d c , the pattern periodicity p diverges as p $ ̃ ∥d − d c∥ −0.5 . For somewhat larger values of d, essentially all periods occur. It is also shown how the vertical and horizontal coordinates of the plate act like Fourier conjugates, so that the squared superconductor order parameter is similar to a probability distribution in a quantum “phase space”.
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