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.

In: Journal of Functional Analysis, Vol. 285, No. 8, 110074, 2023.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Ercolani, NM, Sigal, IM & Zhang, J 2023, 'Ginzburg-Landau equations on non-compact Riemann surfaces', Journal of Functional Analysis, vol. 285, no. 8, 110074. https://doi.org/10.1016/j.jfa.2023.110074

APA

Ercolani, N. M., Sigal, I. M., & Zhang, J. (2023). Ginzburg-Landau equations on non-compact Riemann surfaces. Journal of Functional Analysis, 285(8), [110074]. https://doi.org/10.1016/j.jfa.2023.110074

Vancouver

Ercolani NM, Sigal IM, Zhang J. Ginzburg-Landau equations on non-compact Riemann surfaces. Journal of Functional Analysis. 2023;285(8). 110074. https://doi.org/10.1016/j.jfa.2023.110074

Author

Ercolani, Nicholas M. ; Sigal, Israel Michael ; Zhang, Jingxuan. / Ginzburg-Landau equations on non-compact Riemann surfaces. In: Journal of Functional Analysis. 2023 ; Vol. 285, No. 8.

Bibtex

@article{95b24cc34c8b4bf88042e2e080a0eb3d,
title = "Ginzburg-Landau equations on non-compact Riemann surfaces",
abstract = "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.",
keywords = "Bifurcation theory, Elliptic equations on Riemann surfaces, Ginzburg–Landau equations, Superconductivity",
author = "Ercolani, {Nicholas M.} and Sigal, {Israel Michael} and Jingxuan Zhang",
note = "Publisher Copyright: {\textcopyright} 2023 The Author(s)",
year = "2023",
doi = "10.1016/j.jfa.2023.110074",
language = "English",
volume = "285",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "8",

}

RIS

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