Title: Lischitz conitinuity of the IDS for one dimensional alloy type potentials with small support

Ivan Veselić

Abstract:

We discuss 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 Lipschitz conitinuity of the IDS, and thus 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.

References:

• W. Kirsch, I. Veselić:
  Existence of the density of states for one-dimensional alloy-type potentials with small support, arXiv.org preprint math-ph/0204030 , 2002
  In: R. Weder et al. (Editors) Proceedings of the QMath-8 Conference on Mathematical results in Quantum Mechanics in Taxco, Mexico, December 2001, AMS, Contemporaty Mathematics Vol. 307
• I. Veselić:
  Lokalisierung bei zufällig gestörten periodischen Schrödingeroperatoren in Dimension Eins, diploma thesis, 1996