Dynamical Localization for the Singular Anderson Model in ℤ^d

2023/07/04 by Nishant Rangamani, Rangamani, Nishant, Xiaowen Zhu +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Anderson impurity model #Anderson localization #Bernoulli's principle #Combinatorics #Discrete mathematics #Distribution (mathematics) #Dynamical systems theory #Energy (signal processing) #Energy spectrum #FOS: Mathematics #FOS: Physical sciences #Lattice (music) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #Statistical physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2307.01608

openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the ℤ^d lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the ℤ² and ℤ³ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes.

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