Ginzburg-Landau equations on non-compact Riemann surfaces
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Ginzburg-Landau equations on non-compact Riemann surfaces. / Ercolani, Nicholas M.; Sigal, Israel Michael; Zhang, Jingxuan.
I: Journal of Functional Analysis, Bind 285, Nr. 8, 110074, 2023.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Ginzburg-Landau equations on non-compact Riemann surfaces
AU - Ercolani, Nicholas M.
AU - Sigal, Israel Michael
AU - Zhang, Jingxuan
N1 - Publisher Copyright: © 2023 The Author(s)
PY - 2023
Y1 - 2023
N2 - We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations.
AB - We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations.
KW - Bifurcation theory
KW - Elliptic equations on Riemann surfaces
KW - Ginzburg–Landau equations
KW - Superconductivity
UR - http://www.scopus.com/inward/record.url?scp=85163888621&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2023.110074
DO - 10.1016/j.jfa.2023.110074
M3 - Journal article
AN - SCOPUS:85163888621
VL - 285
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 8
M1 - 110074
ER -
ID: 359650980