Ginzburg-Landau equations on non-compact Riemann surfaces
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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.
Original language | English |
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Article number | 110074 |
Journal | Journal of Functional Analysis |
Volume | 285 |
Issue number | 8 |
Number of pages | 52 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© 2023 The Author(s)
- Bifurcation theory, Elliptic equations on Riemann surfaces, Ginzburg–Landau equations, Superconductivity
Research areas
ID: 359650980