Limit distribution with a combination of density functions for a 2-state quantum walk

Takuya Machida

Published 2010-10-18, updated 2013-07-21Version 4

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk in certain intervals. In the usual QWs starting from the origin, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present some limit distributions for the walk.