Well-posedness and scattering of the Chern-Simons-Schrödinger system

Zhuo Min Harold Lim (Cambridge, UK)

The Chern-Simons-Schrödinger system is a gauge-covariant version of the cubic nonlinear Schrödinger equation in two space dimensions. It describes the effective dynamics of a large system of nonrelativistic

charged quantum particles in the plane, interacting with each other and also with a self-generated long-range electromagnetic field. I will present my recent work establishing well-posedness in the energy space and scattering for the defocusing system, which describes a repulsive binary interaction. The scattering result is surprising from a physical point of view, and reflects subtle cancellations in the long-range electromagnetic interactions

Back to Programme