Work

Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$

Year: 2023

Type: preprint

Abstract: We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ 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 $\mathbb{Z}^2$ and $\mathbb{Z}^3$ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2307.01608

Authors: Rangamani, Nishant, Zhu, Xiaowen

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of California, Irvine, Division of Mathematical Sciences

Awards: G1357031149, Spectral Transitions and Critical Phenomena, Waves and Topology in Quantum Materials, G5881782221, G5928049936, FRG: Collaborative Research: Non-Perturbative Analysis for Multi-Dimensional Quasiperiodic Systems, G7308789069, G7462286394

OpenAlex ID: W4383469047

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