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.