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Journal of the Physical Society of Japan

Ballistic Quantum Walk in a Discrete One-Dimensional System

Takasi Endo, 真一 小佐野, Kouichi Toyoshima, Yutaka Hirayoshi

Published Jun 10, 2009• 4 citations
Publisher

Abstract

A continuous-time quantum walk in a one-dimensional discrete system is considered. There are interactions (\hbar v/\Delta x) between adjacent sites, where Δ x denotes the lattice spacing. If the initial state is spread over N sites, the packet travels ballistically with velocity v for N ≫1.
DOI
10.1143/jpsj.78.064004

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A continuous-time quantum walk of a phase-modulated wave packet is considered in a one-dimensional equispacing lattice {| k >| k ∈ Z }. The interaction ℏc/Δx\hbar c/\Delta xℏc/Δx between adjacent sites drives the packet unidirectionally, where Δ x denotes the lattice spacing. If the initial state is spread over N consecutive sites and phase-modulated by exp (i k θ), the packet travels ballistically with a velocity v = (1 - N -1 ) c cos θ.
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