arXiv subjects

Armen Sergeev

Publications and source records attributed to Armen Sergeev.

2 recordsLinked to original sources

arXiv2022

Ginzburg-Landau equations and their generalizations

The Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It was understood later on that these equations play an important role also in various problems of mathematical physics. We mention here the extension of these equations to compact Riemann surfaces and Riemannian 4-manifolds. A separate interesting topic is the scattering theory of vortices reducing to the study of hyperbolic Ginzburg-Landau equations. In this review we tried to touch these interesting topics with some unsolved problems.

math-ph↗

arXiv2017

Seiberg-Witten theory as a complex version of Abelian Higgs model

The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2+1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg--Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex (2+2)-dimensional version of the (2+1)-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg--Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in (2+1)-dimensional case.

math-ph↗