The Ginzburg-Landau functional on complex line bundles: Gamma-convergence and asymptotics for critical points
by
Giacomo Canevari(Università di Verona)
→
Europe/Paris
Amphi Schwartz
Amphi Schwartz
Description
The Ginzburg-Landau functional was originally proposed as a model for superconductivity in Euclidean domains. However, invariance with respect to gauge transformations - which is one of the most prominent features of the model - suggests that the functional can be naturally defined in the setting of complex line bundles, where it can be regarded as an Abelian Yang-Mills-Higgs theory. In this talk, we shall consider the Ginzburg-Landau functional on a Hermitian line bundle over a closed Riemannian manifold, in the scaling inherited from superconductivity theory. We shall discuss the asymptotic behaviour, in the so-called "London limit", of minimisers and critical points whose energy grows at most logarithmically in the coupling parameter. The talk is based on a joint work with Federico Dipasquale (Università Federico II, Napoli) and Giandomenico Orlandi (Verona).
