Dynamical Localization of Random Quantum Walks on the Lattice

TL;DR

This paper investigates how randomness induces localization in quantum walks on a lattice, using a fractional moments method adapted for unitary operators, revealing conditions under which quantum states become localized.

Contribution

It extends the fractional moments method to analyze localization in random quantum walks on lattices, providing new insights into their disorder-induced behavior.

Findings

Localization occurs in certain regimes of the random quantum walk model.

The fractional moments method effectively demonstrates localization properties.

Results are analogous to large disorder regimes in other quantum systems.

Abstract

This note describes recent results on the localization properties of Random Quantum Walks on the d-dimensional lattice in a regime analogous to the large disorder regime by means of the Fractional Moments Method adapted to the unitary framework.