Internal Lifshitz tails for discrete Schrödinger operators
type: Item
instance of: scholarly article
title: Internal Lifshitz tails for discrete Schrödinger operators
zbMATH Open document ID: 1141.47029
DOI: 10.1155/IJMMS/2006/91865
author: Hatem Najar
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-07-28T00:00:00Z
full work available at URL: https://eudml.org/doc/54354
review text: The main object under consideration in the paper is the following second-order difference random operator which acts in \(\ell^2 (\mathbb Z^d)\) \[ (H_\omega\psi )(n) = 2d\psi (n) - \sum_{|m-n|=1} \psi (m) + (W_{per} (n) + V_{\omega} (n))\psi (n). \] Hamiltonians with a potential energy, which is the sum of periodic and random ones, give the examples of models with gaps in the spectrum for which the investigation of the internal Lifshitz tails is a natural problem. For such operators the integrated density of states (IDS) exists and its topological support is equal to the almost sure spectrum. The main goal of the paper is to determine the behavior of the IDS near the gap edges and to prove that is has a Lifshitz behavior if and only if the IDS of a well-chosen periodic operator is nondegenerate at the same edges. An application to the Anderson localization is given.
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 5304379
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5304379