Transport and localization in random media: theory and applications

Mean-Field Limits for Ginzburg--Landau vortices and related problem

Sylvia Serfaty

New York University


Ginzburg--Landau type equations are models for superconductivity, superfluidity, Bose--Einstein condensation. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions, and which interact like Coulomb particles. We will present new results on the derivation of mean field limits for the dynamics of many vortices starting from the parabolic Ginzburg--Landau equation or the Gross-Pitaevskii (= Schr\"odinger Ginzburg--Landau) equation, as well as results and questions on the situation with random environment, and similar results for the discrete problem of Coulomb-interacting particles.