Non-local Minami-type estimates for a class of quasi-periodic media

TL;DR

This paper extends previous work on Anderson localization in quasi-periodic media by establishing a non-local Minami estimate, enhancing understanding of eigenvalue distributions in deterministic Hamiltonians.

Contribution

It introduces a non-local Minami estimate for quasi-periodic Hamiltonians, building upon earlier KAM-based localization results.

Findings

Proves a non-local Minami eigenvalue estimate for quasi-periodic media.

Enhances understanding of eigenvalue statistics in deterministic Hamiltonians.

Builds on previous exponential localization results using KAM methods.

Abstract

This paper is a follow-up of our earlier work [11] where a uniform exponential Anderson localization was proved for a class of deterministic (including quasi-periodic) Hamiltonians with the help of a variant of the KAM (Kolmogorov--Arnold--Moser) approach. Building on [11], we prove for the same class of operators a non-local variant of the Minami eigenvalue concentration estimate.