Thomas Hupfer, Hajo Leschke, Simone Warzel
Upper bounds on the density of states of single Landau levels
broadened by Gaussian random potentials
(223K, postscript)
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.