On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials
The author considers a family of random Schrödinger operators with magnetic fields. Such operators arise in quantum models of disordered systems. Spectral properties of such operators and the so-called integrated density of states (IDS) are investigated. The main purpose of this paper is to study the asymptotic behaviour of the IDS (Lifshitz type asymptotics) for two types of the random Schrödinger operators. The author uses the functional analytic methods. He uses the Cwikel-Lieb- Rosenbljum and Lieb-Thirring bounds for the number of negative eigenvalues of Schrödinger operators to prove the upper estimates for the IDS. Recently Ueki (preprint) following the path integral approach has studied a similar problem and obtained similar results.
scientific article; zbMATH DE number 469058