Phase transition of an open quantum walk

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced 2012. Indeed, some limit distributions have demonstrated and most of them are described by Gaussian distributions. We operate an walk on $\mathbb{Z}=\left\{0, \pm 1, 2,\ldots\right\}$ with parameterized operations this paper, study its 1st 2nd moments so we find standard deviation. The deviation tells us whether the walker shows diffusive or ballistic behavior, which results a phase transition walker.