Localization for magnetic quantum walks

TL;DR

This paper proves Anderson localization for magnetic quantum walks with Diophantine frequencies, providing the first such result in this setting and analyzing the eigenfunctions' asymptotics.

Contribution

It establishes the first localization result for all Diophantine frequencies in magnetic quantum walks and quasi-periodic CMV models.

Findings

Proves Anderson localization for all Diophantine frequencies.

Derives sharp asymptotics of localized eigenfunctions.

First localization result in magnetic quantum walk setting.

Abstract

We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from 2D quantum walk model subject to an external magnetic field. This is the first localization result for all Diophantine frequencies in the magnetic quantum walk and the quasi-periodic CMV setting. We also obtain sharp asymptotics of the localized eigenfunctions.