New theory of diffusive and coherent nature of optical wave via a quantum walk

TL;DR

This paper introduces a new theoretical framework linking diffusive and coherent behaviors in one-dimensional wave mechanics through quantum walks, supported by numerical evidence of localization and suppression of coherence.

Contribution

It presents a novel theory connecting diffusive and coherent wave properties using quantum walk models, incorporating recent localization findings.

Findings

Randomized localized matrices suppress coherence

Localization phenomenon induces diffusive behavior

Numerical simulations support the theory

Abstract

We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno, Quantum Inf. Proc. (2010) 9, 405-418), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature.