Renormalized energy of interacting Ginzburg�Landau vortex filaments

• Autores: Manuel del Pino, Michal Kowalczyk
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 647-665
• Idioma: inglés
• DOI: 10.1112/jlms/jdm126
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• Resumen

  • We consider the Ginzbug�Landau energy in a cylinder in 3, and a canonical approximation for critical points with an assembly of n2 periodic vortex lines near the axis of the cylinder. We find a formula for the energy which, up to a large additive constant and to leading order, is the action functional of the n-body problem with a logarithmic potential in 2, the axis variable playing the role of time. A special family of rotating helicoidal critical points of the functional is found to be non-degenerate up to the invariances of the problem, and therefore persistent under small perturbations. Our analysis suggests the presence of very complex stationary configurations for vortex filaments, potentially also involving intersecting filaments.