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arXiv · 0804.3347

Lifshitz tails in the 3D Anderson model

Alexander Elgart
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Abstract

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the typical correlation length $ξ_E$ behaves roughly as $O((|E|-σ(E))^{-1/2})$, completing the argument outlined in the unpublished work of T. Spencer.

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Alexander Elgart. 2008-04-21. Lifshitz tails in the 3D Anderson model. https://arxiv.org/abs/0804.3347

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