01-363 Thomas Hupfer, Hajo Leschke, Simone Warzel

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials (223K, postscript) Oct 11, 01

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Abstract. We study a non-relativistic charged particle on the Euclidean plane $ {\mathbbm{R}}^2 $ subject to a perpendicular constant magnetic field and an $ {\mathbbm{R}}^2 $-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space ${\rm L}^2({\mathbbm{R}}^2) $ is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of $ {\mathbbm{R}}^2 $-homogeneous Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.

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