Lifshitz tails for matrix-valued Anderson models

Details Lifshitz tails for matrix-valued Anderson models Lifshitz tails for matrix-valued Anderson models

2011-11-14

arxiv.org/abs/1111.3121v1

Physics

Mathematical Physics

20 pages

Scientific paper

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 $d\geq 1$ and $D\geq 1$. 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.

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