1305.1722 (Norio Konno et al.)

One-dimensional quantum walks via generating function and the CGMV
method    [PDF]

Norio Konno, Etsuo Segawa

We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law" decay around the origin and a "strongly" ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with linear scaling whose density has two delta measures at $x=0$ (the origin) and $x=1$ (the bottom) without continuous parts.

View original: http://arxiv.org/abs/1305.1722