The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity

Abstract

For a charged quantum particle in the Euclidean plane subject to a perpendicular constant magnetic field and repulsive impurities, randomly distributed according to Poisson's law, we determine the leading low-energy fall-off of the integrated density of states in case the single-impurity potential has either super-Gaussian or regular sub-Gaussian long-distance decay. The forms of the resulting so-called magnetic Lifshits tails reflect the great variety of these decays. On the whole, we summarize, unify, and generalize results in previous works of K. Broderix, L. Erdős, D.\ Hundertmark, W. Kirsch, and ourselves.

Contribution to the Proceedings of the International Conference on Partial Differential Equations and Mathematical Physics, Birmingham, Alabama, March 15-19, 1999