It is well-known that Γ-convergence of functionals provides a tool for studying global and local minimizers. Here we present a general result establishing the existence of critical points of a Γ-converging sequence of functionals provided the associated Γ-limit possesses a nondegenerate critical point, subject to certain mild additional hypotheses. We then go on to prove a theorem that describe...

Resistive behaviors at nonzero temperatures (T > 0) reflecting a quantum vortex-glass (VG) transition (the so-called field-tuned superconductor-insulator transition at T = 0) are studied based on a quantum Ginzburg-Landau (GL) action for a s-wave pairing case containing microscopic details. The ordinary dissipative dynamics of the pair-field is assumed on the basis of a consistency between the ...

We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for MgB2, is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies for two bands influence the in-plane Hc2 in a different way at high and low temperatures. This caus...

We study the asymptotic limit of solutions of the Ginzburg-Landau equations in two dimensions with or without magnetic field. We first study the Ginzburg-Landau system with magnetic field describing a superconductor in an applied magnetic field, in the “London limit” of a Ginzburg-Landau parameter κ tending to ∞. We examine the asymptotic behavior of the “vorticity measures” associated to the v...

Suppose that ω ⊂ Ω ⊂ R. In the annular domain A = Ω \ ω̄ we consider the class J of complex valued maps having degree 1 on ∂Ω and ∂ω. It was conjectured in [5] that the existence of minimizers of the Ginzburg-Landau energy Eκ in J is completely determined by the value of the H-capacity cap(A) of the domain and the value of the Ginzburg-Landau parameter κ. The existence of minimizers of Eκ for al...

In a simply connected two dimensional domain Ω, we consider Ginzburg-Landau minimizers u with zero degree Dirichlet boundary condition g ∈ H1/2(∂Ω;S1). We prove uniqueness of u whenever either the energy or the Ginzburg-Landau parameter are small. This generalizes a result of Ye and Zhou requiring smoothness of g. We also obtain uniqueness when Ω is multiply connected and the degrees of the vor...

We report a systematic study of both quantum and classical geometrically frustrated Ising models with competing ordering mechanism. The ordering comes in the classical case from a coupling of two-dimensional (2D) layers and in the quantum model from the quantum dynamics induced by a transverse field. We develop a microscopic derivation of the Landau–Ginzburg–Wilson (LGW) Hamiltonian for these m...

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the c...

We study a mixed heat and Schrödinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning...