Existence of the density of states for onedimensional alloytype potentials with small support
Abstract
We study spectral properties of Schrödinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for nonnegative single site potentials with small support is proven. It implies the existence and local uniform boundedness of the density of states. Our estimate is valid for all bounded energy intervals. Wegner estimates play a key role in an existence proof of pure point spectrum.
 Publication:

arXiv eprints
 Pub Date:
 April 2002
 DOI:
 10.48550/arXiv.mathph/0204030
 arXiv:
 arXiv:mathph/0204030
 Bibcode:
 2002math.ph...4030K
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Mathematical Physics;
 35J10;
 35P20;
 81Q10;
 81Q15
 EPrint:
 See also mp_arc, 02144. In a different version to appear in the proceedings of the QMath8 Conference, Taxco, Mexico, 2001