Analysis of Schrodinger operators with random δ magnetic fields

我们给出了具有安德森型或泊松型随机δ磁场的薛定谔算子的谱的范围，并估计了朗道能级的简并度。证明了安德森情形的Lifshitz尾。我们还研究了庞加莱上半平面上具有Delta磁场的薛定谔算子，并估计了有限Delta场的朗道能隙中本征值的数量，以及晶格情况下的朗道能级的简并度。

We give the range of the spectrum of the Schrodinger operators with random delta magnetic fields of the Anderson type, or of the Poisson type, and estimate the degeneracy of the Landau levels. We prove the Lifshitz tail for the Anderson case. We also study the Schrodinger operators with delta magnetic fields on the Poincare upper half plane, and estimate the number of eigenvalues in Landau gaps for finite delta fields, and the degeneracy of the Landau levels for the lattice case.