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

Published 11 Jun 2022 in math-ph, math.MP, and math.PR | (2206.05545v2)

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.

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