Supersymmetric Cluster Expansions and Applications to Random\n Schr "odinger Operators

2020/03/31 by Luca Fresta, Fresta, Luca
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2004.00145

openalex publication_date 2020/03/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study discrete random Schr "odinger operators via the supersymmetric\nformalism. We develop a cluster expansion that converges at both strong and\nweak disorder. We prove the exponential decay of the disorder-averaged Green's\nfunction and the smoothness of the local density of states either at weak\ndisorder and at energies in proximity of the unperturbed spectrum or at strong\ndisorder and at any energy. As an application, we establish Lifshitz-tail-type\nestimates for the local density of states and thus localization at weak\ndisorder.\n

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