 01394 Thomas Hupfer, Hajo Leschke, Peter Mueller, Simone Warzel
 Existence and uniqueness of the integrated density of states for
Schroedinger operators with magnetic fields
and unbounded random potentials
(331K, PS)
Oct 23, 01

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Abstract. The object of the present study is the integrated density of states
of a quantum particle
in multidimensional Euclidean space which is characterized
by a Schroedinger operator with a constant magnetic field and
a random potential which may be unbounded from above and from below.
For an ergodic random potential
satisfying a simple moment condition,
we give a detailed proof that the
infinitevolume limits of spatial eigenvalue concentrations of
finitevolume operators with different boundary conditions exist almost surely.
Since all these limits are
shown to coincide with the expectation of the trace of the spatially
localized spectral family of the infinitevolume operator,
the integrated density of states is almost surely nonrandom
and independent of the chosen boundary condition.
Our proof of the independence of the boundary condition
builds on and generalizes certain results
obtained
by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335371] and
S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136152].
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