Arithmetic version of anderson localization for quasiperiodic Schr\"odinger operators with even cosine type potentials

TL;DR

This paper introduces a new method to establish Anderson localization in quasiperiodic Schrödinger operators, specifically for models with cosine potentials, large coupling, and Diophantine conditions, advancing understanding in mathematical physics.

Contribution

It presents a novel approach to prove Anderson localization for a class of quasiperiodic Schrödinger operators with cosine potentials, expanding the theoretical framework.

Findings

Proves Anderson localization for large coupling constants.

Applies to models with Diophantine frequencies and phases.

Extends localization results to even $C^2$ cosine potentials.

Abstract

We propose a new method to prove Anderson localization for quasiperiodic Schr\"odinger operators and apply it to the quasiperiodic model considered by Sinai and Fr\"ohlich-Spencer-Wittwer. More concretely, we prove Anderson localization for even $C^2$ cosine type quasiperiodic Schr\"odinger operators with large coupling constants, Diophantine frequencies and Diophantine phases.