Vortices in the Magnetic Ginzburg-Landau Model

By Etienne Sandier, Sylvia Serfaty. 2006

463 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6319cb1fd822a8ecd218cd09b22c586d2172032d

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In Atomic and Molecular Physics, and Optics

In Computer Networks and Communications

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Citations in the corpus

Gamma-convergence of gradient flows on Hilbert and metric spaces and applications (2011, methodology): “in the weak sense of measures, where ∇A denotes ∇− iA (see [SS4], Chapter 6).”
Coulomb Gases and Ginzburg - Landau Vortices (2014, background): “For estimates in the dual of Hölder spaces, see the statement in [SS4].”
On a Fractional Ginzburg–Landau Equation and 1/2-Harmonic Maps into Spheres (2013, unknown): “…symmetric bilinear form associated to E(·, ω), we observe that the restriction of (−∆) 12 v to H 1/2 00 (ω;R m) corresponds to the first variation of the energy E(v, ω) with respect to pertubations supported in ω, i.e., 〈 (−∆) 12 v, ϕ 〉 ω = [ d dt E(v + tϕ, ω) ] t=0 (2.8) for all ϕ ∈ H1/200 (ω;Rm).”
The Crystallization Conjecture: A Review (2015, background): “Under some constraints on the magnetic field, there is a finite number of vortices which behave like classical particles interacting via the (twodimensional) Coulomb potential and submitted to a harmonic confining potential [134, 212,213,221,222].”
Gradient theory for plasticity via homogenization of discrete dislocations (2008, result): “Our result is very much in the spirit of earlier results on the asymptotic analysis for the Ginzburg–Landau model for superconductivity as the number of vortices goes to infinity, done by Jerrard and Soner in [16], and by Sandier and Serfaty in [23] (see also [24] and the references therein).”
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals (2013, methodology): “In [69] it was shown that the next-order corrections are related to a “renormalized energy” denoted W—so named in reference to the procedure used in its definition and related functionals used in Ginzburg-Landau theory [9, 65], but the derivation of this object was restricted to dimension 2 due to a”
From the Ginzburg-Landau Model to Vortex Lattice Problems (2010, methodology): “For a more detailed mathematical presentation of the functional, one may refer to [SS4] and the references therein.”
2D Coulomb Gases and the Renormalized Energy (2012, background): “The case where V (x) is quadratic arises for instance as the interaction energy for superconducting vortices in the Ginzburg-Landau theory, in the regime where their number is fixed, bounded (see [SS2], Chapter 11).”