Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590015 | Journal of Functional Analysis | 2014 | 41 Pages |
Abstract
We consider a particular class of families of multi-dimensional lattice Schrödinger operators with deterministic (e.g., quasi-periodic) potentials generated by the “hull” given by an orthogonal series over the Haar wavelet basis on the torus of arbitrary dimension, with expansion coefficients considered as independent parameters. In the strong disorder regime, we prove Anderson localization for generic operator families and show that all localized eigenfunctions are unimodal and feature uniform exponential decay away from their respective localization centers. We also prove a variant of the Minami estimate for deterministic potentials and simplicity of the spectrum.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Victor Chulaevsky,