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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 91865, 8 pages
http://dx.doi.org/10.1155/IJMMS/2006/91865

Internal Lifshitz tails for discrete Schrödinger operators

Département de Mathématiques Physiques, I.P.E.I. Monastir, Monastir 5000, Tunisia

Received 22 March 2005; Revised 14 May 2006; Accepted 6 August 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider random Schrödinger operators Hω acting on l2(d). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. A possible application of the result to get Anderson localization is given.