Stefan Teufel: Beyond linear response: A macroscopic Ohm law for quantum Hall currents

par Stefan Teufel

vendredi 18 sept. 2026, 09:30 → 12:00 Europe/Paris

Fokko Du Cloux (UCBL)

I will present a recent result establishing a macroscopic form of Ohm’s law for Hall currents in zero-temperature lattice systems of interacting fermions. The main challenge is to go beyond formal linear-response calculations: one must first define the current produced by a spatially extended electric field directly in the thermodynamic limit and then control its dependence on the field strength. We show that the resulting current is linear in the applied field up to errors smaller than any power of the field strength. The argument is based on non-equilibrium almost-stationary states, which provide a mathematical description of the metastable states created by such perturbations.

 

The first part of the talk will recall the physical setting of quantum Hall experiments, discuss the mathematical questions they raise, and survey recent rigorous developments concerning Hall response in interacting systems. After the break, I will formulate the main result in more detail and explain the new ideas behind its proof.