# Regularity properties of bulk and edge current densities at positive temperature

@inproceedings{Moscolari2022RegularityPO, title={Regularity properties of bulk and edge current densities at positive temperature}, author={Massimo Moscolari and Benjamin B St{\o}ttrup}, year={2022} }

We consider magnetic Schrödinger operators describing a quantum Hall effect setup both in the plane and in the half-plane. First, we study the structure and smoothness of the operator range of various powers of the half-plane resolvent. Second, we provide a complete analysis of the diamagnetic current density at positive temperature: we prove that bulk and edge current densities are smooth functions and we show that the edge current density converges to the bulk current density faster than any…

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