Advances in Mathematical Physics
Volume 2009 (2009), Article ID 679827, 15 pages
doi:10.1155/2009/679827
Research Article

The Integrated Density of States for an Interacting Multiparticle Homogeneous Model and Applications to the Anderson Model

Frédéric Klopp1,2 and Heribert Zenk3

1LAGA, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France
2Institut Universitaire de France, 75005 Paris, France
3Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstraße 39, 80333 München, Germany

Received 8 July 2008; Revised 9 October 2008; Accepted 13 January 2009

Academic Editor: Valentin Zagrebnov

Copyright © 2009 Frédéric Klopp and Heribert Zenk. 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

For a system of n interacting particles moving in the background of a “homogeneous” potential, we show that if the single particle Hamiltonian admits a density of states, so does the interacting n-particle Hamiltonian. Moreover, this integrated density of states coincides with that of the free particle Hamiltonian. For the interacting n-particle Anderson model, we prove regularity properties of the integrated density of states by establishing a Wegner estimate.