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

preprint2022arXivOpen access

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

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Dynamical Localization for Random Band Matrices up to W≪N1/4W\ll N^{1/4}W≪N1/4

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