Renormalized energy of interacting Ginzburg-Landau vortex filaments

2008 ◽  
Vol 77 (3) ◽  
pp. 647-665 ◽  
Author(s):  
Manuel Del Pino ◽  
Michał Kowalczyk
Keyword(s):  
Ginzburg Landau ◽  
Vortex Filaments ◽  
Renormalized Energy

ASYMPTOTIC BEHAVIOR OF THE GINZBURG-LANDAU FUNCTIONAL ON COMPLEX LINE BUNDLES OVER COMPACT RIEMANN SURFACES

1996 ◽  
Vol 08 (03) ◽  
pp. 457-486
Author(s):  
GIANDOMENICO ORLANDI
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Chern Class ◽  
Riemann Surfaces ◽  
Line Bundles ◽  
Complex Line ◽  
Ginzburg Landau ◽  
Renormalized Energy ◽  
Compact Riemann Surfaces ◽  
Complex Line Bundles

Motivated by the works of F. Bethuel, H. Brezis, F. Hélein [5] and of F. Bethuel, T. Rivière [6], an asymptotic analysis is carried out for minimizers of the Ginzburg-Landau functional depending on a parameter ε, in the more general case of complex line bundles with prescribed Chern class over compact Riemann surfaces. Such a functional describes a 2-dimensional abelian Higgs model and is also related to phenomena in superconductivity. A suitable renormalized energy is defined which characterizes the singularities (degree one vortices) of the limiting configuration.

scholarly journals LORENTZ SPACE ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY

2012 ◽  
Vol 14 (04) ◽  
pp. 1250027 ◽  
Author(s):  
SYLVIA SERFATY ◽  
IAN TICE
Keyword(s):  
Lorentz Space ◽  
Vortex Lattice ◽  
Construction Method ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Optimal Estimates ◽  
Renormalized Energy ◽  
Funct Anal ◽  
Math Phys

In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier–Serfaty [From the Ginzburg–Landau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz space estimates for the Ginzburg–Landau energy, J. Funct. Anal. 254(3) (2008) 773–825], which couples the "ball construction method" to estimates in the Lorentz space L2,∞.

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