The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length (Q6082524)

The work addresses a particular case of the magnetic Ginzburg-Landau functional, which contains an oscillating pinning term when the latter exhibits oscillations much faster than the coherence length of the system. The physical origin of such a problem relates to the influence of specific impureness and vortices on the phase transition. Ginzburg-Landau energy asymptotics are considered for 2D and 3D cases as well as for the pinned Allen-Cahn energy. The main result consists of the kind of homogenization approach respectively to the pinning term (either periodic or stochastic), which simplifies operating with the functional's minimizers.