论文标题
散装和边缘电流密度在正温度下的规律性特性
Regularity properties of bulk and edge current densities at positive temperature
论文作者
论文摘要
我们考虑了磁性schrödinger操作员，描述了平面和半平面中的量子厅效应。首先，我们研究了半个平面分辨率的各种功率的操作员范围的结构和平滑度。其次，我们对正温度下的磁管电流密度进行了完整的分析：我们证明了散装和边缘电流密度是平滑的函数，并且我们表明，边缘电流密度比在距边界的逆距离内的任何多项式收敛到散装电流密度。我们的证明基于量规协变量磁扰动理论以及对半平面上磁性schrödinger算子功能的积分内核的详细分析。
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.
