Lifshitz tails for alloy type models in a constant magnetic field

Details Lifshitz tails for alloy type models in a constant magnetic field Lifshitz tails for alloy type models in a constant magnetic field

2010-05-05

arxiv.org/abs/1005.0832v2

Mathematics

Spectral Theory

Scientific paper

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type $e^{-\log^2|E-2bq|}$.

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