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

2024/12/19 by Sofiia Dubova, Kevin Yang, Dubova, Sofiia +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2412.15207

Abstract

We study a class of Gaussian random band matrices of dimension N × 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 ≫ 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 ≫ N^8/11.

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• A Block Reduction Method for Random Band Matrices with General Variance Profiles

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