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arXiv · 2412.15207

Quantum diffusion and delocalization in one-dimensional band matrices via the flow method

Sofiia Dubova·Kevin Yang
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Abstract

We study a class of Gaussian random band matrices of dimension $N \times N$ and band-width $W$. We show that delocalization holds for bulk eigenvectors and that quantum diffusion holds for the resolvent, all under the assumption that $W \gg N^{8/11}$. Our analysis is based on a flow method, and a refinement of it may lead to an improvement on the condition $W \gg N^{8/11}$.

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Sofiia Dubova, Kevin Yang. 2024-12-19. Quantum diffusion and delocalization in one-dimensional band matrices via the flow method. https://arxiv.org/abs/2412.15207

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