International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 17, Article ID 91865, 8 pages
doi:10.1155/IJMMS/2006/91865

Internal Lifshitz tails for discrete Schrödinger operators

Abstract

We consider random Schrödinger operators Hω acting on l2(ℤd). 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.