The Ginzburg-Landau Functional with Vanishing Magnetic Field

Bernard Helffer (1, 2) , Ayman Kachmar (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Faculty of Sciences [Lebanese University] | Faculté des Sciences [Université Libanaise]

We study the infimum of the Ginzburg-Landau functional in a two dimensional simply connected domain and with an external magnetic field allowed to vanish along a smooth curve. We obtain an energy asymptotics which is valid when the Ginzburg-Landau parameter is large and the strength of the external field is below the third critical field. Compared with the known results when the external magnetic field does not vanish, we show in this regime a concentration of the energy near the zero set of the external magnetic field. Our results complete former results obtained by K. Attar and X.B. Pan–K.H. Kwek.

Domaines: Mathématiques [math]

Bernard Helffer, Ayman Kachmar. The Ginzburg-Landau Functional with Vanishing Magnetic Field. Archive for Rational Mechanics and Analysis, 2015, 218, pp.55 - 122. ⟨10.1007/s00205-015-0856-z⟩. ⟨hal-01434785⟩