Lifshitz tails for matrix-valued Anderson models

Abstract

This paper is devoted to the study of Lifshitz tails for a continuous matrix-valued Anderson-type model $H_{\omega }$ acting on $L^2(\R^d)\otimes \C^{D}$, for arbitrary $d\ge 1$ and $D\ge 1$. We prove that the integrated density of states of $H_{\omega }$ has a Lifshitz behavior at the bottom of the spectrum. We obtain a Lifshitz exponent equal to $-d/2$ and this exponent is independent of $D$. It shows that the behaviour of the integrated density of states at the bottom of the spectrum of a quasi-d-dimensional Anderson model is the same as its behaviour for a d-dimensional Anderson model.

24 pages

References in corpus (3)

• Localization for a matrix-valued Anderson model
• Hölder continuity of the IDS for matrix-valued Anderson models
• Lifshitz tails for alloy type models in a constant magnetic field