Ginzburg-Landau Model Of Superconductivity Research Articles

Excited States of “Elementary” Particles in Gauge-Higgs Theories

We show that the gauge and scalar fields which surround static ions in the Ginzburg-Landau model of superconductivity have a spectrum of excitations which are potentially observable. This ties in with earlier results along these lines found in a variety of gauge Higgs theories. Excitations of this type would appear as a mass spectrum of the “elementary” particles in the theory.

Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential

We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain oscillatory patterns which are consistent with the Little-Parks effect. We study also the same problem but for a regularization of the Aharonov-Bohm potential, which leads to an interesting Aharonov-Bohm like magnetic field, and we prove that the transition between superconducting and normal solutions is not monotone too. Our results explore a mechanism to derive the Aharonov-Bohm magnetic potential starting from a step magnetic field, thereby presenting a new aspect of magnetic steps, besides their favoring of the celebrated edge states.

Existence and uniqueness for a Ginzburg-Landau system for superconductivity

We prove the existence of a unique solution for a time-dependent Ginzburg-Landau model in superconductivity under the Coulomb gauge. Also we prove the uniform-in-\(\epsilon\) well-posedness of the solution, where \(\epsilon\) is the coefficient of the double-well potential energy.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/17/abstr.html

Well-posedness of a 2D time-dependent Ginzburg-Landau superconductivity model

Well-posedness of a 2D time-dependent Ginzburg-Landau superconductivity model

A regularity criterion to the time-dependent Ginzburg-Landau model for superconductivity in [formula omitted

In this paper, we prove a regularity criterion ψ,A∈W:={(ψ,A)|∇ψ∈L2(0,T;Ln), A∈L∞(0,T;Ln)∩L2pp−n(0,T;Lp)} with n<p≤∞, for the nD(n≥3) time-dependent Ginzburg-Landau model in superconductivity. Finally, we show that this criterion holds true when n=3 or 4.

Charged and neutral fixed points in the O(N)⊕O(N) model with Abelian gauge fields

In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity, the existence of an infrared stable charged fixed point ensures that there is a parameter range where the superconducting phase transition is second order, as opposed to fluctuation-induced first order as one would infer from the Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a two-field generalization of the Abelian-Higgs model, where two N-component fields are coupled to two gauge fields and to each other, using the functional renormalization group. Focusing mostly on three dimensions, in the neutral case, this is a model for two-component Bose-Einstein condensation, and we confirm the fixed-point structure established in earlier works using different methods. The charged model is a dual theory of two-dimensional dislocation-mediated quantum melting. We find the existence of three charged fixed points for all N>2, while there are additional fixed points for N=2.

UNIFORM WELL-POSEDNESS FOR A TIME-DEPENDENT GINZBURG-LANDAU MODEL IN SUPERCONDUCTIVITY

We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient 0 < $\epsilon$ < 1 in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when $\epsilon=0$.

Global well-posedness of the time-dependent Ginzburg–Landau superconductivity model in curved polyhedra

We prove global existence and uniqueness of weak solutions for the time-dependent Ginzburg–Landau equations in a three-dimensional curved polyhedron which is not necessarily convex, where the gradient of the magnetic potential may not be square integrable. Preceding analyses all required the gradient of the solution to be square integrable, which is only true in convex or smooth domains.

Global strong solutions to the time-dependent Ginzburg-Landau model in superconductivity with four new gauges

Global strong solutions to the time-dependent Ginzburg-Landau model in superconductivity with four new gauges

Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge

We first prove the uniqueness of weak solutions to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if , which is a critical space for some positive constant . We also prove the global existence of solutions for the Ginzburg-Landau system with magnetic diffusivity or . Finally, we prove the uniform bounds with respect to of strong solutions in space dimensions . Consequently, the existence of the limit as can be established.

Ginzburg-Landau Vortices, Coulomb Gases, and Renormalized Energies

This is a review about a series of results on vortices in the Ginzburg-Landau model of superconductivity on the one hand, and point patterns in Coulomb gases on the other hand, as well as the connections between the two topics.

On Abrikosov Lattice Solutions of the Ginzburg-Landau Equation

Building on earlier work, we have given in [29] a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity and shown that the triangular lattice gives the lowest energy per lattice cell. After [29] was published, we realized that it proves a stronger result than was stated there. This result is recorded in the present paper. The proofs remain the same as in [29], apart from some streamlining.

Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity

We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L 2 initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139–166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L 2 initial data.

Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field \( H_{C_1 } \) which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.

Uniqueness of weak solutions of time-dependent 3-D Ginzburg-Landau model for superconductivity

We prove the uniqueness of weak solutions of the time-dependent 3-D Ginzburg-Landau model for superconductivity with (Ψ0, A0) ∈ L2(Ω) initial data under the hypothesis that (Ψ, A) ∈ C([0, T]; L3(Ω)) using the Lorentz gauge.

Global existence of weak solutions of a time-dependent 3-D Ginzburg-Landau model for superconductivity

We study an initial boundary value problem for a time-dependent 3-D Ginzburg-Landau model of superconductivity. We prove the existence of global weak solutions with L 2 initial data and, hence, solve an open problem mentioned in [1].

Non-linear Surface Superconductivity for Type II Superconductors in the Large-Domain Limit

The Ginzburg-Landau model for superconductivity is considered in two dimensions. We show, for smooth bounded domains, that superconductivity remains concentrated near the surface when the applied magnetic field is decreased below HC3 as long as it is greater than HC2. We demonstrate this result in the large-domain limit, i.e, when the domain's size tends to infinity. Additionally, we prove that for applied fields greater than HC2, the only solution in ℝ2 satisfying normal-state conditions at infinity is the normal state. The above results have been proved in the past for the linear case. Here we prove them for non-linear problems.

Some Existence and Uniqueness Results for a Stationary Ginzburg-Landau Model of Superconductivity

In this article we study the steady problem for gauge invariant Ginzburg-Landau equations obtained from a Gibbs free energy functional expressed in terms of observable variables and prove some existence and uniqueness results.

The mixed boundary condition for the Ginzburg Landau model in thin films

The mixed boundary condition for the Ginzburg Landau model of superconductivity is considered in thin films. A simplified model is derived in the asymptotic limit of very small thickness. We also show that under certain conditions there is no nucleation of superconductivity at all.

Critical properties of the topological Ginzburg-Landau model

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed point structure and eventually the region of first order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the $\nu$ exponent does not vary very much from the XY value, $\nu_{XY}=0.67$. This shows that the Chern-Simons term does not affect considerably the XY scaling of superconductors. We discuss briefly the possible phenomenological applications of this model.