Anderson localization for generic deterministic operators

TL;DR

This paper proves Anderson localization for a broad class of deterministic lattice Schrödinger operators with random-like potentials, using a Multi-Scale Analysis approach, and establishes bounds on spectral spacings.

Contribution

It introduces a novel application of Multi-Scale Analysis to deterministic operators with complex potentials, extending localization results.

Findings

Proves Anderson localization for generic deterministic operators.

Establishes Minami-type bounds for spectral spacings.

Demonstrates localization in the strong disorder regime.

Abstract

We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary measurable space. Using a variant of the Multi-Scale Analysis, we prove Anderson localization for generic ensembles in the strong disorder regime and establish an analog of Minami-type bounds for spectral spacings.