Dynamical Localization for Random Band Matrices up to $W\ll N^{1/4}$

Abstract

We prove that a large class of $N\times N$ Gaussian random band matrices with band width $W$ exhibits dynamical Anderson localization at all energies when $W\ll N^{1/4}$. The proof uses the fractional moment method and an adaptive Mermin--Wagner style shift.

25 pages