Ginzburg-Landau Equations on Non-compact Riemann Surfaces

Autor:	Ercolani, Nicolas M., Sigal, Israel Michael, Zhang, Jingxuan
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs 35Q56 (primary) 35J66 (secondary)
Zdroj:	Journal of Functional Analysis 285 (2023) 110074
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jfa.2023.110074
Popis:	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. Comment: added Section 7 on extension to degenerate case; reformulated main result; minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.14179 Zobrazit plný text záznamu View this record from Arxiv