Domenico Monaco

https://sites.google.com/view/dmonaco 

Speaker at the Spring Time in Mathematical Quantum Physics workshop (May 2025, UBC)

TITLE: Purely linear response of the quantum Hall current to space-adiabatic perturbations

ABSTRACT: In the quantum Hall effect, when a 2D electron gas is brought out of equilibrium by an electric field of small intensity, the transverse current responds exhibiting a quantized conductance. This conductance, seen as the linear response of the current in the strength of the perturbing electric field, can be expressed through the so-called double commutator formula, involving only the equilibrium ground state of the system, and furthermore all higher-order terms in this response vanish. I will show how these results can be proved by means of a recently-developed technique which characterizes a non-equilibrium almost-stationary state (NEASS) of the perturbed quantum system. This technique applies to continuum models of quantum Hall systems in the 1-body approximation, as well as to weakly interacting lattice fermions.

Based on joint works with G. Marcelli, T. Miyao, S. Teufel, and M. Wesle.