Mimicking spatial localization in dynamical random environment

TL;DR

This paper investigates how time-dependent phase noise in a 1D quantum walk model can induce quasi-localized states, revealing a novel form of localization driven by temporal randomness rather than spatial disorder.

Contribution

It demonstrates the emergence of quasi-localization in a quantum walk due to phase noise, a phenomenon not previously observed with time-dependent noise.

Findings

Wider phase noise intervals increase localization effects

Localized states can be controlled via noise parameters

Localization occurs with time-dependent noise, unlike traditional spatial Anderson localization

Abstract

We study the role played by noise on the QW introduced in [1], a 1D model that is inspired by a two particle interacting QW. The noise is introduced by a random change in the value of the phase during the evolution, from a constant probability distribution within a given interval. The consequences of introducing such kind of noise depend on both the center value and the width of that interval: a wider interval manifests as a higher level of noise. For some range of parameters, one obtains a quasi-localized state, with a diffusive speed that can be controlled by varying the parameters of the noise. The existence of this (approximately) localized state for such kind of time-dependent noise is, to the best of our knowledge, totally new, since localization (i.e., Anderson localization) is linked in the literature to a spatial random noise.