

International conference "Geometrical Methods in Mathematical Physics"
December 17, 2011 10:45, Moscow, Lomonosov Moscow State University






Adiabatic limit in Ginzburg–Landau equations.
A. G. Sergeev^{} ^{} Steklov Mathematical Institute of the Russian Academy of Sciences

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Abstract:
Hyperbolic Ginzburg–Landau equations are the Euler–Lagrange equations for
the (2+1)dimensional Abelian Higgs model, arising in gauge field theory.
Static solutions of these equations are called vortices and their moduli
space is described by Taubes. The structure of the moduli space of dynamic
solutions is far from being understood but there is an heuristic method, due
to Manton, allowing to construct solutions of Ginzburg–Landau equations
with small kinetic energy. The idea is that in the adiabatic limit dynamic
solutions should converge to geodesics on the moduli space of vortices in
the metric, generated by kinetic energy functional. According to Manton's
adiabatic principle, any solution of dynamic equations with a sufficiently
small kinetic energy can be obtained as a perturbation of some geodesic of
this type. Our talk is devoted to the mathematical justification of this
principle.
Materials:
gmmp2011_agsergeev.pdf (3.3 Mb)
Language: English

