English

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

Mathematical Physics 2024-08-16 v2 math.MP Spectral Theory

Abstract

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the Zd\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 Z2\mathbb{Z}^2 and Z3\mathbb{Z}^3 cases with Bernoulli single site probability distribution, our results imply SDL in these regimes.

Cite

@article{arxiv.2307.01608,
  title  = {Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$},
  author = {Nishant Rangamani and Xiaowen Zhu},
  journal= {arXiv preprint arXiv:2307.01608},
  year   = {2024}
}

Comments

28 pages

R2 v1 2026-06-28T11:21:41.731Z