Localization of a multi-dimensional quantum walk with one defect
Mathematical Physics
2017-03-16 v1 math.MP
Spectral Theory
Abstract
In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schr\"{o}dinger operator with variable coefficients, which is analyzed using the Feshbach map.
Keywords
Cite
@article{arxiv.1703.04558,
title = {Localization of a multi-dimensional quantum walk with one defect},
author = {Toru Fuda and Daiju Funakawa and Akito Suzuki},
journal= {arXiv preprint arXiv:1703.04558},
year = {2017}
}