We study the dynamics of a generalization of a quantum coin walk on the line, which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations for recurrence phenomena observed by Bouwmeester et al. [Phys. Rev. A 61, 13410 (1999)] in their optical Galton board experiment, and a description of a stroboscopic quantum walk given by Buerschaper and Burnett [quant-ph/0406039] through numerical simulations. We also provide heuristic explanations for the behavior of our model which show, in particular, that its dynamics can be viewed as a discrete version of Bloch oscillations.

• Received 16 July 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.180601