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The aim of this article is to study the magnetic Ginzburg-Landau functionalwith an oscillating pinning term. We consider here oscillations of the pinningterm that are much faster than the coherence length \(\varepsilon>0\) which isalso the inverse of the Ginzburg-Landau parameter. We study both the case of aperiodic potential and of a random stationary ergodic one. We prove that we canreduce the study of the problem to the case where the pinning term is replacedby its average, in the periodic case, and by its expectation with respect tothe random parameter in the random case. In order to do that we use adecoupling of the energy due to Lassoued-Mironescu. This leads us to the studyof the convergence of a scalar positive minimizer of the Ginzburg-Landau energywith pinning term and with homogeneous Neumann boundary conditions. We proveuniform convergence of this minimizer towards the mean value of the pinningterm by using a blow-up argument and a Liouville type result for non-vanishingentire solutions of the real Ginzburg-Landau/Allen-Cahn equation, due toFarina.

The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length