Thomas Hupfer, Hajo Leschke, Peter Mueller, Simone Warzel
The Absolute Continuity of the Integrated Density of States 
for Magnetic Schr{\"o}dinger Operators with Certain Unbounded 
Random Potentials
(282K, Postscript)

ABSTRACT.  The object of the present study is the integrated density of states 
of a quantum particle 
in multi-dimensional Euclidean space which is characterized 
by a Schr{\"o}dinger operator with magnetic field and 
a random potential which may be unbounded from above and below. 
In case that the magnetic field is constant 
and the random potential is ergodic and admits a so-called 
one-parameter decomposition, 
we prove the absolute continuity of the integrated density 
of states and provide explicit upper bounds on its derivative, 
the density of states. 
This local Lipschitz continuity of the integrated density of states 
is derived by establishing a Wegner estimate for finite-volume 
Schr\"odinger operators which holds for rather general magnetic fields 
and different boundary conditions. 
Examples of random potentials to which the results apply are 
certain alloy-type and Gaussian random potentials. 
Besides we show a diamagnetic inequality for Schr{\"o}dinger 
operators with Neumann boundary conditions.