Weak limit theorem of a twophase quantum walk with one defect
Abstract
We attempt to analyze a onedimensional spaceinhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW "the twophase QW", which we treated concerning localization theorems [10]. The twophase QW has been expected to be a mathematical model of the topological insulator [16] which is an intense issue both theoretically and experimentally [3,5,11]. In this paper, we derive the weak limit theorem describing the ballistic spreading, and as a result, we obtain the mathematical expression of the whole picture of the asymptotic behavior. Our approach is based mainly on the generating function of the weight of the passages. We emphasize that the timeaveraged limit measure is symmetric for the origin [10], however, the weak limit measure is asymmetric, which implies that the weak limit theorem represents the asymmetry of the probability distribution.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.4309
 Bibcode:
 2014arXiv1412.4309E
 Keywords:

 Mathematical Physics
 EPrint:
 15 pages, 3 figures