2022/01/21 by Massimo Moscolari, Moscolari, Massimo, Benjamin B. Støttrup +1
Computer Science · Mathematics · #35J10 #47A10 #81Q10 #81V70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2201.08803
openalex publication_date 2022/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 polynomial in the inverse distance from the boundary. Our proofs are based on gauge covariant magnetic perturbation theory and on a detailed analysis of the integral kernels of functions of magnetic Schrödinger operators on the half-plane.