Quantum Random Walks of Waves

TL;DR

This paper explores the behaviors of quantum walks of waves, particularly plane waves, revealing differences from classical and particle quantum walks, and demonstrates their application in evolving general wave packets like Gaussian ones.

Contribution

It introduces the study of quantum walks of waves, analyzing plane wave behaviors and their use in wave packet evolution, which is a novel extension beyond particle-based quantum walks.

Findings

Quantum walks of plane waves differ significantly from classical and particle quantum walks.

Intermediate measurements influence the behavior of wave quantum walks.

Quantum walks of plane waves can be used to model the evolution of Gaussian wave packets.

Abstract

The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum walks of waves. Firstly, we show the behaviors of the quantum walks of plane wave, which are largely different from the counterparts of either the classical or the quantum walks of particles. Two situations - with and without intermediate time measurements of the walks are considered. At last, it is shown that the quantum walks of plane wave can be used to calculate the evolution of the general wave packets, e.g., Gaussian wave packet.