Characterization of anomalous diffusion in one-dimensional quantum walks

TL;DR

This paper investigates how different coin operations influence anomalous diffusion in one-dimensional quantum walks, revealing the roles of quantum coherence and interference in diverse diffusion behaviors.

Contribution

It demonstrates how specific coin operations can control diffusion types in quantum walks and clarifies the impact of quantum interference on anomalous diffusion.

Findings

Homogeneous and accelerated quantum walks show superdiffusive behavior.

Disorders induce localization, leading to subdiffusive and normal diffusion.

Quantum coherence is key to anomalous diffusion phenomena.

Abstract

Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By controlling the action of quantum coin operation on the corresponding coin degree of freedom of the walker, one can demonstrate control over the diffusion behavior. In this work, we report different forms of coin operations on quantum walks exhibiting anomalous diffusion behavior. Homogeneous and accelerated quantum walks display superdiffusive behavior, whereas uncorrelated static and dynamic disorders in the evolution induce strong and weak localization of the particle indicating subdiffusive and normal diffusive behavior. The role played by the interference effects in the spreading of the walker has remained elusive and our aim in this work is to present the interplay between quantum coherence and mean squared displacement of the walker. We employ two reliable measures of coherence for conclusively establishing the role of quantum interference as the driving force behind the anomalous diffusive behavior in the dynamics of quantum walks.