The stability of magnetic vortices

Authors
Gustafson, S Sigal, IM
Citation
S. Gustafson et Im. Sigal, The stability of magnetic vortices, COMM MATH P, 212(2), 2000, pp. 257-275
Citations number
25
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
212
Issue
2
Year of publication
2000
Pages
257 - 275
Database
ISI
SICI code
0010-3616(200007)212:2<257:TSOMV>2.0.ZU;2-S
Abstract
We study the linearized stability of n-vortex (n is an element of Z) soluti ons of the magnetic Ginzburg-Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = +/-1) are stable for all values of the c oupling constant, lambda, and we prove that the higher-degree vortices (\ n \ greater than or equal to 2) are stable for lambda < 1, and unstable for lambda > 1. This resolves a long-standing conjecture (see, eg, [JT]).