Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

Details Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

2000-11-07

arxiv.org/abs/math-ph/0011010v3

Journal of Mathematical Physics 42 (2001) 5626-5641

Physics

Mathematical Physics

16 pages, to appear in "Journal of Mathematical Physics"

Scientific paper

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of 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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