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The energy of Ginzburg–Landau vortices

Published online by Cambridge University Press:  16 April 2002

Y. N. OVCHINNIKOV  and
I. M. SIGAL
Y. N. OVCHINNIKOV
Affiliation:
Landau Institute, Moscow, Russia
I. M. SIGAL
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3, Canada email: sigal@math.utoronto.ca
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Abstract

We consider the Ginzburg–Landau equation in dimension two. We introduce a key notion of the vortex (interaction) energy. It is defined by minimizing the renormalized Ginzburg–Landau (free) energy functional over functions with a given set of zeros of given local indices. We find the asymptotic behaviour of the vortex energy as the inter-vortex distances grow. The leading term of the asymptotic expansion is the vortex self-energy while the next term is the classical Kirchhoff–Onsager Hamiltonian. To derive this expansion we use several novel techniques.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 2 , April 2002 , pp. 153 - 178
Copyright
2002 Cambridge University Press

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