Existence of the density of states for one-dimensional alloy-type potentials with small support

Werner Kirsch; Ivan Veselic'

Existence of the density of states for one-dimensional alloy-type potentials with small support

Mathematical Physics 2007-05-23 v1 Analysis of PDEs math.MP

Authors: Werner Kirsch , Ivan Veselic'

Abstract

We study spectral properties of Schr\"odinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative 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.

Keywords

density of states schrödinger operators alloy-type potentials wegner estimate random potentials pure point spectrum

Cite

@article{arxiv.math-ph/0204030,
  title  = {Existence of the density of states for one-dimensional alloy-type potentials with small support},
  author = {Werner Kirsch and Ivan Veselic'},
  journal= {arXiv preprint arXiv:math-ph/0204030},
  year   = {2007}
}

Comments

See also mp_arc, 02-144. In a different version to appear in the proceedings of the QMath-8 Conference, Taxco, Mexico, 2001

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