Lifshitz tails in the 3D Anderson model

Details Lifshitz tails in the 3D Anderson model Lifshitz tails in the 3D Anderson model

2008-04-21

arxiv.org/abs/0804.3347v1

Physics

Mathematical Physics

24 pages, 3 figures, to appear in DMJ

Scientific paper

Consider the 3D Anderson model with a zero mean and bounded i.i.d. random potential. Let $\lambda$ be the coupling constant measuring the strength of the disorder, and $\sigma(E)$ the self energy of the model at energy $E$. For any $\epsilon>0$ and sufficiently small $\lambda$, we derive almost sure localization in the band $E \le -\sigma(0)-\lambda^{4-\epsilon}$. In this energy region, we show that the typical correlation length $\xi_E$ behaves roughly as $O((|E|-\sigma(E))^{-1/2})$, completing the argument outlined in the unpublished work of T. Spencer.

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