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.