Lines vortices in the U(1) - Higgs model

Riviere, Tristan. "Lines vortices in the U(1) - Higgs model." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 77-167. <http://eudml.org/doc/197265>.

@article{Riviere2010,
abstract = { For a given U(1)-bundle E over M = $\lambda _\{2\}$\{x1, ..., xn\}, where the xi are n distinct points of $\lambda _\{2\}$, we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The results presented here were announced in [12]. },
author = {Riviere, Tristan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Non linear PDE / elliptic equations / abelian gauge theory / Ginzburg-Landau equations / Higgs field / variationnal problem on fiber bundle / variationnal problem in superconductivity / vortices and singularities / harmonic maps.; Higgs field; Ginzburg-Landau equations},
language = {eng},
month = {3},
pages = {77-167},
publisher = {EDP Sciences},
title = {Lines vortices in the U(1) - Higgs model},
url = {http://eudml.org/doc/197265},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Riviere, Tristan
TI - Lines vortices in the U(1) - Higgs model
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 77
EP - 167
AB - For a given U(1)-bundle E over M = $\lambda _{2}${x1, ..., xn}, where the xi are n distinct points of $\lambda _{2}$, we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The results presented here were announced in [12].
LA - eng
KW - Non linear PDE / elliptic equations / abelian gauge theory / Ginzburg-Landau equations / Higgs field / variationnal problem on fiber bundle / variationnal problem in superconductivity / vortices and singularities / harmonic maps.; Higgs field; Ginzburg-Landau equations
UR - http://eudml.org/doc/197265
ER -