Lifshitz tails for matrix-valued Anderson models
| Autor: | Boumaza, Hakim, Najar, Hatem |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages |
| Databáze: | arXiv |
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