Ballistic Quantum Walk of a Phase-Modulated Wave Packet
Takasi Endo, Ken'ichiro Katsuki, Kouichi Toyoshima, Yutaka Hirayoshi · Journal of the Physical Society of Japan · 2012
A continuous-time quantum walk of a phase-modulated wave packet is considered in a one-dimensional equispacing lattice {| k >| k ∈ Z }. The interaction \(\hbar c/\Delta x\) between adjacent sites drives the packet unidirectionally, where Δ x denotes the lattice spacing. If the initial state is spread over N consecutive sites and phase-modulated by exp (i k θ), the packet travels ballistically with a velocity v = (1 - N -1 ) c cos θ.