  We study the dynamics of a generalization of 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 to
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 walks given by Buershaper 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.
