Joint BCAM-UPV/EHU Analysis and PDE seminar: Bulk-edge correspondence at positive temperature

Abstract
We consider a quantum Hall effect setting, involving unbounded random Schrödinger operators with long range magnetic fields.

Our main result is a general formula, which states that the derivative with respect to the external magnetic field of a given physical bulk quantity equals the expectation of an edge velocity operator associated to the same observable. No spectral (mobility) gaps are required.

In particular, we show that the grand canonical bulk magnetization is -up to a universal constant- equal to an averaged edge charge current flowing parallel to the cut, at all temperatures. By taking the zero temperature limit and imposing a gap condition, we recover the usual equality between bulk and edge Hall conductivities.

This is joint ongoing work with M. Moscolari and S. Teufel.

Link to the session: https://zoom.us/j/97475811544?pwd=OHR4YXFzbzlyVlE4LytXbmlxaDU2QT09

More info at https://sites.google.com/view/apdebilbao/home