# Lifshitz tails in the 3D Anderson model - Mathematical Physics

Abstract: Consider the 3D Anderson model with a zero mean and bounded i.i.d. randompotential. Let $\lambda$ be the coupling constant measuring the strength of thedisorder, and $\sigmaE$ the self energy of the model at energy $E$. For any$\epsilon>0$ and sufficiently small $\lambda$, we derive almost surelocalization in the band $E \le -\sigma0-\lambda^{4-\epsilon}$. In thisenergy region, we show that the typical correlation length $\xi E$ behavesroughly as $O|E|-\sigmaE^{-1-2}$, completing the argument outlined in theunpublished work of T. Spencer.

Author: Alexander Elgart

Source: https://arxiv.org/