Séminaire Physique mathématique ICJ

Adiabatic Deformations of Quantum Hall Droplets

by Blagoje Oblak (Ecole Polytechnique, Paris)

Fokko du Cloux (Bâtiment Braconnier)

Fokko du Cloux (Bâtiment Braconnier)

The study of two-dimensional droplets of electrons in a strong magnetic field lies at the heart of the quantum Hall effect. In this talk, I present recent results on area-preserving deformations of such droplets, implemented through unitary "quantomorphisms" that appear in geometric quantization. Time-dependent deformations of this kind give rise to Berry phases that can remarkably be written in closed form despite the fact that the underlying parameter space is infinite-dimensional. In particular, I argue that a large class of deformations that generalize squeezing and shearing probe the edge modes of the system and provide a bulk-edge correspondence for Hall viscosity.
(Based on 2212.12935)